The C-intercept is the point at which the function crosses the C-axis, then it is at t=0.
As we know two points on the line: (-20, 200) and (30,0), and we found previously the slope m=-4.
We can use the slope-intercept form of the equation of a line to find the C-intercept as follows:
[tex]C=m\cdot t+b[/tex]Where (t,C) is any point on the line, m is the slope and b is the C-intercept.
By replacing the know values we can solve for b:
[tex]\begin{gathered} 0=-4\cdot30+b \\ 0=-120+b \\ \text{Add 120 to both sides} \\ 0+120=-120+b+120 \\ 120=b \end{gathered}[/tex]Therefore,
(1 point) Find the slope of the line containing the points f(-3) = 9 and f(9) = -10.
The most appropriate choice for slope of a line will be given by-
Slope of the line = [tex]\frac{-19}{12}[/tex]
What is slope of a line?
At first it is important to know about line.
Line is a geometrical object that has only length but no breadth and no height.
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta\\[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
m = [tex]tan\theta[/tex]
If the line passes through ([tex]x_1,y_1[/tex]) and ([tex]x_2, y_2[/tex]) , then
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex]x_1 = -3, y_1 = 9. x_2 = 9, y_2 = -10[/tex]
Slope = [tex]\frac{-10 - 9}{9 - (-3))}[/tex]
= [tex]\frac{-19}{12}[/tex]
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f(x) = 8x + 1, g(x) = 4x - 2
Find (fg)(x).
f(g(x)) for the given equation f(x)=8x+1 and g(x)=4x-2 is 32x-15 using substitution method of solving the equation.
What is equation?An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. It is a formula that expresses the connection between two expressions on each side of a sign.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
given,
f(x)=8x+1
g(x)=4x-2
f(g(x))=8(4x-2)+1
=32x-16+1
f(g(x))=32x-15
Hence, this is required f(g(x)) for the given two equations.
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The point Q lies on the segment PR.
Find the coordinates of Q so that PQ is
Check
17/0 of PR.
P(-3,4)
Coordinates of Q: D
Q (?, ?)
R (24,-32)
X
Save For Later
Submit
Answer:
Step-by-step explanation:
it would be 42,32 i know
Find the area of a triangle bounded by the
y
axis, the line
f
(
x
)
=
4
−
1
5
x
, and the line perpendicular to
f
(
x
)
that passes through the origin.
The area of a triangle bounded by the region will be 11.95 sq. units.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that,
y = f(x) = 7- (4/5)x
Slope,m = -4/5
The slope of the perpendicular lines is,
[tex]\rm m_p = \frac{-1}{\dfrac{-4}{5}} \\\\ m_ p = \dfrc{5}{4}[/tex]
The equation of the perpendicular line passing through the origin is
[tex]\rm y = \frac{5}{4} x[/tex]
The equation can be written as,
[tex]\rm \frac{5}{4} x = 7 - \frac{4}{5} x \\\\ 25 x = 140 - 16 x \\\\ 41x = 140 \\\\ x = \dfrac{140}{41} \\\\ y = \frac{175}{41}[/tex]
As a result, the y-intercept of the line is,
[tex]\rm y =7- \dfrac{4}{5}x \\\\ y= 7[/tex]
The triangle is bounded by the points (0,0), (0,7), and (140/41, 175/41)
The area of the triangle is,
[tex]\rm A= \frac{1}{2} \times 7 \times \dfrac{140}{141} \\\\ A = 11.95 \ sq. unit[/tex]
Thus, the area of a triangle bounded by the region will be 11.95 sq. unit.
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solve using distributive property ASAP
8(x+2)
The equation 8(x+2) can be expressed using the distributive property as 8x + 16.
What is distributive property?The distributive property can be described as the as the multiplication system of solving a particular expressions easily through the process of distributing another number within the given brackets.
The expression that was given as 8(x+2) , if it so be solved using the distributive property the we will have 8x + 16 because this result means that it has been shared in to part, because the multiplication operation has been performed on the given expression.
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Pls help with number 20
The lengths 8 cm, 14 cm, 15 cm can form a triangle
Explanation:Given 8 cm, 14 cm, 15 cm
These can form a triangle if the sum of any two sides of the triangle is greater than the third side.
8 + 14 > 15
14 + 15 > 8
8 + 15 > 14
Since all the above are true, we conclude that they can form a triangle
Can somebody help me with this please ?
The correct answer is option d, output = 6 - input using coordinate geometry.
What is coordinate geometry?In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.
From the graph, we can see that the coordinates have the values
For x = 1, y = 5
For x = 2, y = 4
For x = 3, y = 3
For x = 4, y = 2
Hence, we can conclude that the output (y) = 6 - input (x)
The correct option is (d) output = 6 - input.
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what is the equation of a line that goes through the points 2, -2 and 0,2
it is vital that we first find the gradient/slope between the points .
⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{2-(-2)}{0-2} \\m=\frac{4}{-2} \\m=-2[/tex]
The general equation of a straight line is given by y=mx+c I will use the points (0,2) to find the value of y since the other variables are found already.
[tex]2=-2(0)+c\\\\c=2[/tex]
⇒This tells us that the equation of the line is y=-2x+2
If AC=19 and BC=7, find the length of AB.
Multiply using the FOIL method.
(8z + 7)(9z-1)
Answer: [tex]72z^{2} +55z-7[/tex]
Step-by-step explanation:
We multiply each component with each other:
8z * 9z = 72z^2
8z * -1 = -8z
9z * 7 = 63z
7 * -1 = -7
We then add it all together, 63z + -8z = 55z and get
[tex]72z^{2} +55z-7[/tex]
can someone help me on this
Answer:
The best estimate for the correlation coefficient is .85.
(-35) divided by 7 =?
Answer:
-5
Step-by-step explanation:
Answer: -5
Step-by-step explanation: -35 divided by 7 is -5
Write the component form of the vector.
Answer:
C , D
Step-by-step explanation:
The component form of a vector is given as < x, y >, where x describes how far right or left a vector is going and y describes how far up or down a vector is going.
The component form of vector C is <1, 5> and the component form of vector D is <8, 2>. The components represent the magnitudes of the vector's displacements in the x and y directions, respectively.
To write the component form of a vector, we simply list its components, which are the numerical values that represent the vector's magnitude and direction in each dimension. In this case, we have vector C with components C<1, 5> and vector D with components D<8, 2>.
The components of a vector represent its position or displacement along the coordinate axes. In a two-dimensional Cartesian coordinate system, the first component represents the displacement along the x-axis (horizontal direction), and the second component represents the displacement along the y-axis (vertical direction).
For vector C, the component form is written as <1, 5>, where the first component is 1 and the second component is 5. This means that vector C has a displacement of 1 unit in the x-direction and 5 units in the y-direction.
Similarly, for vector D, the component form is <8, 2>, indicating a displacement of 8 units in the x-direction and 2 units in the y-direction.
Therefore, the component form of vector C is <1, 5> and the component form of vector D is <8, 2>. The components represent the magnitudes of the vector's displacements in the x and y directions, respectively.
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May I please get help with this. For I have tried multiple times but still could not get the correct answers for them or even plot it on the graph 90 degrees clockwise
To rotate the figure 90 degrees clockwise about a point, every point (x, y) will rotate to (y, -x):
[tex](x,y)\to(y,-x)[/tex]The vertices of the triangle have the following coordinates:
[tex]\begin{gathered} 1=(-5,-1) \\ 2=(-1,-2) \\ 3=(-3,-4) \end{gathered}[/tex]Applying the transformation rule, we have the new coordinates to be:
[tex]\begin{gathered} 1\to(-1,-(-5))=(-1,5) \\ 2\to(-2,-(-1))=(-2,1) \\ 3\to(-4,-(-3))=(-4,3) \end{gathered}[/tex]The transformed image is shown below (the black triangle):
Write an equation in slope-intercept form for the line with slope -4/3 and y-intercept 3
I got that but I’m not sure if it’s right.
Answer:
[tex]y=-\frac{4}{3}x+3[/tex]
A genetic experiment with peas resulted in one sample of offspring that consisted of 434 green peas and 153 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
a) The 90% confidence interval to estimate the percentage of yellow peas is (23.09%, 29.03%.)
b) Based on the confidence interval, the results of the experiment do not appear to contradict the expectation that 25% of the offspring peas would be yellow.
Given:
Confidence level,c = 90% = 0.90
Number of successes, x = 153
Sample size,n = 434 + 153 = 587
a) The sample proportion is the number of successes divided by the sample size is,
p = x/n
p = 153/587
p ≅ 0.2606
For confidence level 1 - α = 0.90, determine [tex]z_{\alpha /2} = z_{0.05}[/tex] utilizing the normal probability table in the appendix
[tex]z_{\alpha /2} = 1.64[/tex]
The margin of error is calculated as:
[tex]E = z_{\alpha /2} \sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]E = 1.64\sqrt{\frac{0.2606(1 -0.2606)}{587} }[/tex]
E ≅ 0.0297
Therefore, the boundaries of the confidence interval are:
p - E = 0.2606 - 0.0297 = 0.2309 = 23.09%
p + E = 0.2606 + 0.0297 = 0.2903 = 29.03%
We are 90% confident that the true percentage of yellow peas is between 23.09% and 29.03%.
b) As 25% is between 23.09% and 29.03%, and 25% of the offspring are expected to be yellow peas and thus the results do not contradict expectations.
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PLS ANSWER THIS MATH PROBLEM!!
Answer:
48[tex]units^{2}[/tex]
Step-by-step explanation:
equations with parenthesis
Answer:b=6
Step-by-step explanation:
A rental car agency charges $240.00 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $477.50
Answer: 950
Step-by-step explanation:
$477.50 - $240.00 = 237.50
$237.50 / $0.25 = 950
In the game, your score grew by 200 points each time you scored. Two expressions below represent your echoes after 12 hits. Find both.
A) 200 + 200 + - - - + 200 +200
—————————————————
12times
B) 200 ⚫️ 200 ⚫️ - - - ⚫️ 200 ⚫️ 200
—————————————————
12times
C) 200 ⚫️ 12
D) 200 + 12
Answer: A and C
Sample Answer: Multiplication is a short way to write repeated addition. So 200 •12 means the same as 200 + 200 + . . . + 200.
Answer:
b
Step-by-step explanation:
A set of average city temperatures in April are normally distributed with a mean of 19.7 Celsius in a standard deviation of two Celsius the average temperature of Kabul is 15 Celsius what proportion of the average city temperatures are lower than that of Kabul?
Answer:
There is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
Step-by-step explanation:
In this question, we are to calculate the proportion of average city temperatures lower than that of Kabul.
Firstly, we shall calculate the z score
Mathematically;
z = (value - mean)/standard deviation = 15 - 19.7/2 = -4.7/2 = -2.35
so we are to calculate the probability of; P(z< -2.35) = 0.0094
This means there is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
help meeeeeeeeee
12 Answer:
Evaluate the expression: 8-6+4
13 Answer:
Evaluate the expression: 16÷(4-2)-3
14 Answer:
Check whether the given number is a solution of the equation:
3x + 5 = 17; x=2
a. solution is correct
b. solution is incorrect
15 Answer:
Check whether the given number is a solution of the equation:
4y - 7 = 3y - 4; y=3
a. solution is correct
b. solution is incorrect
16 Answer:
Check whether the given number is a solution of the inequality:
2m - 3 < 4; 2
a. number is a solution
b. number is not a solution
17 Answer:
Check whether the given number is a solution of the inequality:
5 + 2n ≥ 12; 0
a. number is a solution
b. number is not a solution
Answer:
Step-by-step explanation:
13) 8 - 6 + 4 = 2 + 4 = 6
14) 16÷(4-2)-3 = 16÷2 - 3 = 8 - 3 = 5
15) 3x + 5 = 17
3x = 17 - 5
3x = 12
x = 4 ≠ 2
b. solution is incorrect
16)4y - 7 = 3y - 4
4y - 3y = -4 + 7
y = 3
a. solution is correct
17) 2m - 3 < 4
2m < 4 + 3
2m < 7
m < 3.5
2 < 2.5, so a. number is a solution
18 ) 5 + 2n ≥ 12
2n ≥ 12 - 5
2n ≥ 7
n ≥ 3.5
0 is not greater than equal to 3.5, so b. number is not a solution
Find the volume of this rectangular pyramid Be sure to include the correct unit in your answer
Okay, here we have this:
Considering the provided rectangular pyramid, we are going to calculate the requested volume, so we obtain the following:
Then, we are going to use the following formula to find the volume of this rectangular pyramid:
V=(abH)/3
Replacing:
V=(abH)/3
V=(5cm*6cm*7cm)/3
V=(210cm^3)/3
V=70 cm^3
Finally we obtain that the volume of the rectangular prism is 70 cm^3.
If the ratio of red objects to blue objects is 3 : 1, what precent of the objects are red?
Answer:
75%
Step-by-step explanation:
If the ratio of red:blue is 3:1, then there are 4 (some multiple of 4) in all.
The ratio of red:total is 3:4
3/4 is .75, times by 100 to convert to a percent.
.75 × 100 is 75%
Is 47/8 less then 23/4
Answer:
no
Step-by-step explanation:
Generally you can't really compare two functions with a different denomination, and you want to multiply the fractions by some fraction: [tex]\frac{a}{a}[/tex] which simplifies to one so we're not changing the value of the fraction at all but it helps so we have the same denominator.
You'll notice we can multiply 4 by 2 to get 8, which would give us the same denominator as 8.
[tex]\frac{23}{4}*\frac{2}{2}=\frac{46}{8}[/tex]
Now it's much easier to compare: [tex]\frac{47}{8}\text{ and }\frac{46}{8}[/tex] and here all we have to compare is the numerators, and obviously 47 is greater than 46 so the 47/8 is greater than the 23/4. This means 47/8 is not less than 23/4
The balance on a credit card, that charges a 15.5%
APR interest rate, over a 1 month period is given in
the following table:
Days 1-3: $200 (initial balance)
Days 4-20: $300 ($100 purchase)
Days 21-30: $150 ($150 payment)
What is the finance charge, on the average daily
balance, for this card over this 1 month period?
finance charge = $ [?]
Round to the nearest hundredth.
Enter
4
Finance charge = $93.00
What is finance charge of credit card?The interest you'll pay on a loan is defined as a finance charge, and it's most commonly used in the context of credit card debt. A financing fee is computed by taking your annual percentage rate, or APR, the amount you owe, and the time period into account.
Given that,
Interest rate = 15.5%
Date: 1-3 (3 days)
Average daily balance = amount paid × days
= $200 × 3 = $600
Date: 4-20 (17 days)
Average daily balance = amount paid × days
= $300 × 17 = $5100
Date: 21-30 (10 days)
Average daily balance = amount paid × days
= $150 × 10 = $1500
So, total average daily balance for the month
= $(600+5100+1500)
= $7200
Now, the finance charge = $7200 × (15.5÷12)
= $93.00
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Find the sample standard deviation.
15 42 53 7 9 12 14 28 47
The answer to your question is s. sqrt (316.9) = 17.8 when you take the square root of that number. As a result, the correct response is 17.8.
This is further explained below.
What is the sample standard deviation?Generally, Because you need to calculate the sample standard deviation to answer the question, use the following formula:
[tex]s = \sqrt {{ \sum of x - \bar x}{(n - 1} }[/tex]
There are 9 numbers, there, so n - 1 = 8
find the mean
[tex]\bar x[/tex]: 15 + 42 + 53 + . . . + 47 = 227. 227 / 9
x= 25.2
After that, deduct one from each number and then square the output, as seen here:
(15 - 25.2) = 104.0 (42 - 25.2)²
= 282.2 (53 - 25.2)²
= 772.8
After that, total up all of those values. The response to this, using this illustration as an example, is
[tex]x=\frac{ 2,535.2}{ 8}[/tex]
x= 316.9.
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In exercises 11-14 ,find m<1,m<2, and m<3.explain your reasoning ?
The measure of angles 1, 2, and 3 in exercise 11. are 100°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 12. are 47°, 133°, and 47°.
The measure of angles 1, 2, and 3 in exercise 13. are 80°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 14. are 94°, 86°, and 94°.
For 11. part:
Considering a transversal p that cuts two parallel lines l and m,
Each pair of internal angles on the same side of a transversal that intersects two parallel lines are supplementary.
m∠1 + 80° = 180°
m∠1 = 180° - 80°
m∠1 = 100°
Similarly, m∠1 + m∠2 = 180°
⇒ 100° + m∠2 = 180°
⇒m∠2 = 180° - 100°
⇒m∠2 = 80°
and also, m∠2 + m∠3 = 180°
⇒ 80° + m∠3 = 180°
⇒m∠3 = 180° - 80°
⇒m∠3 = 100°
Therefore, m∠1 = 100°, m∠2 = 80° and m∠3 = 100°.
For 12. part:
m∠3 + 133° = 180°(interior angles are supplementary)
m∠3 = 180° - 133°
⇒m∠3 = 47°
m∠2 = 133°(alternate interior angles)
The angle vertically opposite to 133° would also be 133°.
So, 133° + m∠1 = 180°( interior angles are supplementary)
m∠1 = 47°
Therefore, m∠1 = 47°, m∠2 = 133° and m∠3 = 47°.
For 13. part:
m∠3 = 100° (vertically opposite angle)
Let's assume the angle adjacent to ∠3 is x.
m∠3 + m ∠x = 180° (Linear pair property)
100° + m ∠x = 180°
m ∠x = 180° - 100°
m ∠x = 80°
Therefore, m∠1 = m∠2 = m ∠x = 80°(Corresponding angles are equal.)
For 14. part:
m∠1 + 86° = 180°(co-interior angles are supplementary)
m∠1 = 180°- 86° = 94°
The angle vertically opposite to m∠1 is also equal to 94°.
94° + m∠1 = 180°(co-interior angles are supplementary)
m∠2 = 86°
Similarly, the angle vertically opposite to m∠2 is also equal to 86°.
86° + m∠3 = 180°(co-interior angles are supplementary)
m∠3 = 94°
Therefore, m∠1 = 94°, m∠2 = 86° and m∠3 = 94°.
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Which value of xis in the domain of f(x) = √x – 7?
We are looking for values of x that will not make the equation undefined .Obviously the function has restrictions we have to make sure that x-7 is always ≥0 because it is under a square root
[tex]x-7\geq 0\\x\geq 7[/tex]
The domain of the function is all the real numbers greater or equal to 7 .
x≥7 ε R
What is the slope of the line represented by the equation 2x+3y=-12
Answer:
-2/3
Step-by-step explanation:
I graphed it