The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the following formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the points (-11, 12) and (5, 4), we get:
m = (4 - 12) / (5 - (-11)) = -8 / 16 = -1/2
So the slope of the line passing through (-11, 12) and (5, 4) is -1/2.
1. Ben purchased a used car for $25,500 and had to pay 9.5% sales tax. How much did he pay in sales tax?
2. The cost of an ad in a local paper is given by the piecewise function.
x≤5)
c(x) = {40 +7(x-4), x> 5}
Find the difference in cost between a one-line ad and a four-line ad.
The difference in cost between a one-line ad and a four-line ad is $14.
What is percentage ?
Percentage can be defined as product of ratio of given value, total value and hundred.
To find how much Ben paid in sales tax, we need to first calculate the amount of the sales tax.
The sales tax is 9.5% of the purchase price of the car, which can be expressed as a decimal by dividing by 100:
Sales tax rate = 9.5% = 0.095
To find the amount of sales tax, we can multiply the purchase price by the sales tax rate
Sales tax = 0.095 x $25,500 = $2,422.50
Therefore, Ben paid $2,422.50 in sales tax.
The cost of an ad in a local paper is given by the piecewise function:
c(x) = 40, for x ≤ 5 (one-line ad)
c(x) = 40 + 7(x - 4), for x > 5 (four-line ad)
To find the difference in cost between a one-line ad and a four-line ad, we can subtract the cost of a one-line ad from the cost of a four-line ad:
c(6) - c(1) = (40 + 7(6 - 4)) - 40 = 14
Therefore, the difference in cost between a one-line ad and a four-line ad is $14.
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A study found that a student's GPA, g, is related to the number of hours worked each week, h, by the equation
g = - 0.0007h? + 0.012h + 3.04. Estimate the number of hours worked each week for a student with a GPA of 2.21.
Using the equation provided, you can estimate the number of hours worked each week for a student with a GPA of 2.21. The equation can be rearranged to solve for h, the number of hours worked each week.
h = (g - 3.04) / (0.012 + 0.0007)
Plugging in the GPA of 2.21, we get:
h = (2.21 - 3.04) / (0.012 + 0.0007)
h = -4.83 hours
Therefore, a student with a GPA of 2.21 would need to work an average of -4.83 hours per week in order to achieve that GPA.
¿Que probabilidad hay de que al lanzar dos dados la suma sea 11 en la primera tirada y 5 en la segunda?
Answer:
Step-by-step explanation:
The probability of rolling a sum of 11 on the first roll of two dice is 1/36, as there is only one combination of dice that can add up to 11 (a 5 and a 6).
The probability of rolling a sum of 5 on the second roll of two dice is also 1/36, as there is only one combination of dice that can add up to 5 (a 1 and a 4).
The probability of two independent events occurring is equal to the product of their individual probabilities. So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is:
1/36 * 1/36 = 1/1296
So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is 1/1296.
What is the answer
? I’ve been having triuble
Answer:
120°
Step-by-step explanation:
We need to find the missing angle <SRM
The angles inside a triangle always add up to 180°. So this means:
<TSR+<STR+<TRS=180°
65°+55°+<TRS=180°
120°+<TRS=180°
<TRS=180°-120°=60°
All angles along a straight line add up to 180°. This means:
<TRS+<SRM=180°
60°+<SRM=180°
<SRM=180°-60°=120°
Answer:
120° is the answer please mark. brainly
Jenny swam 8 kilometers against the current in the same amount of time it took her to swim 16 kilometers with the current. The rate of the current was 1 kilometer per hour.
How fast would Jenny swim if there were no current?
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let the time taken by Jeeny in both the cases be " t " ~
Now, during upstream : current flow opposes the flow of swimmer (Jenny)
Let her actual speed without current be " v ", so her speed in current (upstream) will be :
[tex]\qquad \sf \dashrightarrow \: v - 1 \: \: kmph[/tex]
Now, according to formula :
[tex]\qquad \sf \dashrightarrow \: distance = speed \times time[/tex]
[tex]\qquad \sf \dashrightarrow \: 8 = (v - 1)t \: \: \: \: \: - (1)[/tex]
Next, durijg dowstream : current flow supporta the flow of swimmer (Jenny)
So, her speed while going downstream will be :
[tex]\qquad \sf \dashrightarrow \: v +1 \: \: kmph[/tex]
By same formula,
[tex]\qquad \sf \dashrightarrow \: 16 = (v + 1)t \: \: \: \: \: - (2)[/tex]
Now, solve the two equations ~
[ since time taken by her in both the cases is same, we use t in both equations ]
Divide equation (1) by equation (2) :
[tex]\qquad \sf \dashrightarrow \: \dfrac{8}{16} = \dfrac{v - 1}{v + 1} [/tex]
[ t gets canceled out ]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{2} = \dfrac{v - 1}{v + 1} [/tex]
[ cross multiply ]
[tex]\qquad \sf \dashrightarrow \: v + 1 = 2(v - 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: v + 1 = 2v - 2[/tex]
[tex]\qquad \sf \dashrightarrow \: 2v - v = 1 - ( - 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: v = 1 + 2[/tex]
[tex]\qquad \sf \dashrightarrow \: v = 3 \: \: kmph[/tex]
That's the required answer ~ [ Jimmy would swim at the rate of 3 kmph if she there was no current ]
What is the volume 
On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh = 18+24 = 32 in cubic
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
volume of figure 1 = volume of cuboid = lbh = 8*3*1 = 24 in cubic
volume of figure 2= volume of cuboid = lbh = 6*3*1 = 18 in cubic
total volume of figure = total volume of cuboid = lbh = 18+24 = 32 in cubic
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On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh = 18+24 = 32 in cubic
What exactly is a cuboid?In geometry, a cuboid is a solid or three-dimensional form. A cuboid is an 8-vertex, 12-sided polyhedron with 6 rectangular faces. A cuboid is another name for a cuboid. A cube is a six-square-faced cuboid. Books and bricks are examples of items found in boxes. The key distinctions between cubic and cubic are as follows: A cube has six equally sized square faces, as opposed to a cube's rectangular faces. Although the cube and cuboid structures appear similar, they differ in terms of side length, diagonal, and area.
Figure 1 volume = cuboid volume = lbh = 8*3*1 = 24 in cubic
Figure 2 volume = cuboid volume = lbh = 6*3*1 = 18
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please help me ive been struggling for a little bit
Using Pythagorean theorem, The value of cos(S) rounded to the nearest hundredth is approximately 0.78.
What is Triangle like?It is the simplest polygon and a key component in many branches of science and mathematics.
A triangle's three sides can be equilateral, isosceles, scalene, or any other combination of lengths and kinds. An isosceles triangle has a third side that is a different length from the other two sides, while an equilateral triangle has three sides that are all the same length. All three of the sides of a scalene triangle are different lengths.
In triangle STU, right angled at T, we have:
[tex]ST = 6UT = \sqrt{(22)}[/tex]
We can use the Pythagorean theorem to find the length of TU:
[tex]TU^2 = ST^2 + UT^2\\TU^2 = 6^2 + (\sqrt{(22)})^2\\TU^2 = 36 + 22\\TU^2 = 58\\TU = sqrt(58)\\[/tex]
Now, we can use the definition of cosine:
cos(S) = adjacent/hypotenuse
In this case, the adjacent side to angle S is ST and the hypotenuse is TU. Therefore:
[tex]cos(S) = ST/TU\\cos(S) = 6/\sqrt{(58)}[/tex]
To round to the nearest hundredth, we can divide 6 by the rounded value of sqrt(58):
cos(S) ≈ 0.78 (rounded to the nearest hundredth)
Therefore, the value of cos(S) rounded to the nearest hundredth is approximately 0.78.
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HELP PLSSSSSSSSSSSSSSSSSS
Answer: A) 6
Step-by-step explanation:
This is geometry. The two angles are corresponding angles, because they are both cut by the same **transversal line**. When that occurs, corresponding angles are created.
now importantly: corresponding angles are equal to each other, or **congruent**. Knowing this, we can set them equal to each other.
17x+11=19x-1
Solve...
11=2x-1
12=2x
x=6
hope this helps
MM
What is an equation of the line that passes through the points (0, -3) and (0, -8)?
Answer:
Step-by-step explanation:
here is a step-by-step explanation for finding the equation of the line that passes through the points (0, -3) and (0, -8):
Identify the two points that the line passes through: (0, -3) and (0, -8)
Determine the slope of the line: The slope of a line is given by the formula "rise over run," or (y2 - y1) / (x2 - x1). However, in this case, the line is vertical and has an undefined slope.
Write the equation of the line in slope-intercept form: y = mx + b, where "m" is the slope and "b" is the y-intercept. Since the slope of the line is undefined, the equation of the line cannot be written in slope-intercept form.
Write the equation of the line in point-slope form: y - y1 = m(x - x1), where "m" is the slope and (x1, y1) is a point on the line. Since the slope of the line is undefined, the equation of the line cannot be written in point-slope form.
Write the equation of the line as an x-intercept form: The x-intercept form of a line is given by the equation x = a, where "a" is the x-coordinate of the point that the line passes through. In this case, the line passes through the point (0, -3) and (0, -8), so the equation of the line is x = 0.
So, the equation of the line that passes through the points (0, -3) and (0, -8) is x = 0.
Find the indicated outputs for f(x) = 4x - 5x. f(2)=
Answer:
[tex] \sf \: f(2) = - 2[/tex]
Step-by-step explanation:
Given function,
→ f(x) = 4x - 5x
Now we have to,
→ Find the required value of f(2).
Then the value of f(2) will be,
→ f(x) = 4x - 5x
→ f(2) = 4(2) - 5(2)
→ f(2) = 8 - 10
→ [ f(2) = -2 ]
Hence, the value of f(2) is -2.
Circles and answers please just need help please sap
On solving the provided question, we can say that x = central angle = 60 degrees, r = radius = 9 inches and L = 9.42
what are angles?An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.
x = central angle = 60 degrees
r = radius = 9 inches
L = arc length
[tex]L = (x/360)*2*pi*r\\L = (60/360)*2*pi*9\\L = 3*pi\\L = 9.42477796076938\\L = 9.42[/tex]
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Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d. Justify your answer.2x + 4y = f
cx + dy = g."
Not quite sure what is meant by the question "what can you say." My only thought so far is that If the system is consistent, that means x and y have the same value for both equations:
x(2 + c) + y(4 + d) = f + g, which, if c = f+g, fits into the form ax + by = c. But that's about it.
We can know that she can be any value but these 15 times the value of C. The given system is consistent to all the possible values of f and g, the reduction of the row of the augmented matrix must not result in the row of form [0 0 ... 0 | b]where B is nonzero.
By looking the row reduction in the system we can see the 2nd row reduces to [0 0 ...0 | d-15c-g+f]. Since f and g can be any values we can make them both 20 which denotes d - 15 C is equals to zero, or d equals to 15C.
d-15c = 0, or d = 15c.
Therefore we can know that she can be any value but these 15 times the value of C.
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Which of the statements is true about the graph for the system of inequalities?
y ≤-2x
y ≥ 3
A The graph of the boundary line for y ≥ 3 should be dashed.
B Area C should be the shaded region.
C Area A should be the shaded region instead of the region shaded on the graph.
D The equations y < -2x should be an uphill line, not a downhill line.
Answer Option C
The point-slope form of the equation of the line is:
Where m is the slope and b is the intersection with the y-axis.
In the line , you can identify that:
The symbol of the inequality "" indicates that you must shade the region below the boundary line and for the symbols of inequalities "" and "" the line must be solid (Observe the graph attached).
Then the answer is the option C.
please mark me brainliest
Answer:
C
Step-by-step explanation:
Area A should be the shaded region instead of the region shaded on the graph.
2. I am a regular polygon. One of my interior angles is 135°. What size is one of
my exterior angles?
Answer:
45°
Step-by-step explanation:
Given a polygon with an interior angle of 135°, you want to know the measure of the corresponding exterior angle.
Exterior angleAt any given vertex of a polygon, the interior and exterior angles are supplementary:
exterior angle = 180° - interior angle
exterior angle = 180° -135°
exterior angle = 45°
Answer: The sum of the interior angles of a regular polygon can be found using the formula:
(n-2)180°, where n is the number of sides of the polygon.
Let's call the number of sides of the polygon "s".
We know that one of the interior angles is 135°, so we can set up an equation using the formula for the sum of the interior angles:
s * 135° = (s-2)180°
Expanding the right side of the equation:
s * 135° = (s-2) * 180°
s * 135° = s * 180° - 360°
Solving for s:
135° = 180° - 360°/s
135° = 180° - 2 * 180°/s
135° = 180° - 2 * (180°/s)
180° - 135° = 2 * (180°/s)
45° = (180°/s)
So, s = 180° / 45° = 4 sides.
The size of one exterior angle can be found by subtracting each interior angle from 360°:
360° - 135° = 225°.
Therefore, one exterior angle of the polygon is 225°.
Step-by-step explanation:
What was the first target of the huac hearings? communist infiltration in the u. S. State department communist infiltration in the entertainment industry communist influence in the democratic party communist influence in non-governmental organizations.
"Communist infiltration in the entertainment industry" was the first target of the HUAC hearings among the following choices given in the question.
HUAC was created in 1938 to investigate alleged disloyalty and rebel activities on the part of private citizens, public employees and organizations suspected of having Communist ties.
Originally organized as a minor congressional committee investigating domestic subversion, HUAC (also known as the House Un-American Activities Committee) rose to such power in the late 1940's and early 1950's that the mere threat of investigation by it could ruin a person's career. By the time it was abolished in 1975, HUAC had widened its scope of investigation to include almost every aspect of American society.
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can someone help me please hurry
Question 1: Find the distance between the following points: a) (-2,-2) and (-3, -1) b) (-1,-4) and (5, 4)
Answer:
a
Step-by-step explanation:
Given sin 0 = and angle Ø is in Quadrant I, what is the exact value of cos ✪ in simplest form? Simplify all radicals if needed.
Answer:
cosΘ = [tex]\frac{\sqrt{21} }{5}[/tex]
Step-by-step explanation:
using the identity
• sin²Θ + cos²Θ = 1 ⇒ cos²Θ = 1 - sin²Θ
given Θ is in quadrant 1 , then cosΘ > 0
sinΘ = [tex]\frac{2}{5}[/tex] , then
cos²Θ = 1 - ( [tex]\frac{2}{5}[/tex] )² = 1 - [tex]\frac{4}{25}[/tex] = [tex]\frac{25}{25}[/tex] - [tex]\frac{4}{25}[/tex] = [tex]\frac{21}{25}[/tex] , then
cosΘ = [tex]\sqrt{\frac{21}{25} }[/tex] = [tex]\frac{\sqrt{21} }{\sqrt{25} }[/tex] = [tex]\frac{\sqrt{21} }{5}[/tex]
A road is inclined at an angle of 6 . After driving 4950 feet along this road, find the driver's increase in altitude.
The driver increased altitude is 517 feet.
How to find the side of a right triangle?A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the road is inclined at an angle of 6 degrees. After driving 4950 feet along this road, let's find the altitude as follows:
using trigonometric ratios,
sin 6° = opposite / hypotenuse
Therefore,
sin 6° = a / 4950
cross multiply'
a = 4950 sin 6°
a = 4950 × 0.10452846326
a = 517.415893175
Therefore,
a = 517 feet
Altitude = 517 feet
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An initial investment amount P, an annual interest rate r, and a time t are given. Find the future value of the investment
when interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. Then find (e) the doubling time T
for the given interest rate.
P= $1500, r = 3.95%, t = 5 yr
a) The future value of the investment when interest is compounded annually is $
(Type an integer or a decimal. Round to the nearest cent as needed.)
ANSWER ALL PARTS
A, B, C, D, E
The future value of the investment when interest is compounded continuously is; $3408.29
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Given Data
P= $1500, r = 3.95%, t = 5 yr
To Calculate the number of periods: in this case we have 5*12= 60 months.
- The monthly interest rate, we have to divide the annual nominal rate by 12 (the number of periods in the year).
Then, we can calculate the future value as:
A = P (1 + r/n)^nt
A = 1500(1 + 3.95/365)(365)^(5)
P = 1500/ (1 + 0.00010137)^(5)
P = $3408.29
The future value when compounded monthly is $3408.29.
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8. Write the fraction from the number line that is greater than
4
but less than
5
18
3
8
The fractions greater than 5/8 are 6/8, 7/8 and 8/8
The fractions less than 3/8 are 1/8 and 2/8The fractions greater than 3/8 are 4/8, 5/8, 6/8, 7/8 and 8/8How to determine the fractionsFractions greater than 5/8
Using the number line as a guide, we have the following:
Fractions greater = 6/8, 7/8 and 8/8
Fractions less than 3/8
Using the number line as a guide, we have the following:
Fractions less = 1/8 and 2/8
Fractions greater than 3/8
Using the number line as a guide, we have the following:
Fractions greater = 4/8, 5/8, 6/8, 7/8 and 8/8
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Jack works as a waiter and is keeping track of the tips he earns daily. About how much does jack have to earn in tips on sunday if he wants to average $19 a day?.
Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.
Average = (Sum of all values) / (Number of values)
Average = ($19) / (7 days)
Average = ($19) / (7)
Average = $2.71
Sunday = ($2.71) x (7)
Sunday = $19.00 + $76.00
Sunday = $95.00
Jack is working as a waiter and needs to keep track of his tips. He wants to make an average of $19 per day and needs to figure out how much he needs to make on Sunday. To calculate this, he needs to first figure out the average he wants to make per day. For this, he needs to divide the amount he wants to make daily ($19) by the number of days he is working (7). This gives him an average of $2.71 per day. To get to the amount he needs to make on Sunday, he needs to multiply this average by the number of days he is working, which is 7. This gives him an amount of $19.00 + $76.00, which equals $95.00. Thus, Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.
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In isosc tri(ABC),AC=BC,AB=6 in., line segment cd is parrelel to line segment ab, and CD= sqrt(3) in find the perimeter of the isosc triangle
On solving the provided question we can say that median from the vertex in an isosceles triangle is perpendicular to the base.
What is triangle?ƒ(x)=sin(x)
consider Asin(Bx + C) = y +D changes the amplitude of the function (how high or low it is).
if you want to
Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.
Let O be the circle's centre and P be the midpoint of BC. After that, OP LBC.
Let AP =x and PB = CP -y.
Applying Pythagoras theorem in As AP B and OP B, we have
AB2 = BP2 + AP2 and OB2 = OP2 +BP2
Y2 +x2 ... (i) and, 81 = (9 —x)2 + Y2
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The wheel of a car has an outer radius of 25 cm. Calculate: a how far the car has travelled after one complete turn of the wheel, b how many times the wheel turns for a journey of 1 km.
Answer: a) 1.57 m .
b) 637.79 turns
Step-by-step explanation:
a) The circumference of the wheel can be used to determine how far the vehicle has travelled after making one full turn.
Circumference = 2πr = 50π
C = 157 cm
b)By dividing the entire distance traveled by the diameter of the wheel, we can determine how many times the wheel will turn over a ride of 1 km (1000 meters): 1000 m / 1.57 m = 637.79 turns.
How much pure alcohol must a pharmacist add to 10^3 of a 10% alchohol solution to strengthen it to a 70% solution? (ASAP)
Answer:
60% i mean it sounds right
Step-by-step explanation:
Please help me with this question
Answer:
I don't know
Step-by-step explanation:
What is the first quartile of the data set represented by the box plot shown
below?
13 20 25
A. 25
B. 40
C. 20
D. 13
40
48
The first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.
What is the first quartile of the data set?
The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.
Since we have given a box and whisker plot.
As we know about the box and whisker method that :
Left most part of the box represents the first quartile and the rightmost part of the box represents the third quartile.
And the middle value is for median
so, we can conclude that
First quartile = 20
Third quartile = 40
Median = 25
Hence, the first quartile of the data set represented by the box plot shown in the figure is 20 option 'C' is correct.
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A savings account increases from $150 to $159. What is the percent increase of the savings account? Question content area bottom Part 1 The percent increase of the savings account is enter your response here%.
Answer:
6%
Step-by-step explanation:
percent of change formula = difference between new and original values divided by original value, then multiply by 100 to get a percent
(159 - 150) / 150 = 9/150
9/150 = .06 = 6%
Arithmetic Reasoning
How many 5-pound bags of apples can be made from 400 apples, each weighing 1/4 pound?
A
20
B
C
50
100
Answer: To find the total weight of 400 apples, we need to multiply the number of apples by their weight. Each apple weighs 1/4 pound, so 400 apples weigh 400 * (1/4) = 100 pounds.
Since each bag should weigh 5 pounds, we can divide the total weight of apples (100 pounds) by 5 to find the number of bags: 100 / 5 = 20 bags.
So, the answer is 20 bags.
Step-by-step explanation:
Bill works for the stuff-it mailing service. He receives 25 cents for each document he puts together and prepares for mailing. Last week, bill prepared 2,000 documents for mailing for a local politician. He received a check with gross pay of $474 and is certain the amount is incorrect. A. What is bill's correct total piecework pay? b. How much does his boss owe him?.
Using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.
What is meant by the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Once we have determined the value of a single unit, we may multiply that value by the number of units needed to determine the value of the other units. The concept of ratio and proportion is mostly applied using this way. Recognizing the units and values is crucial when using the unitary technique to a problem.
Given,
Money received for each document = 25 cents
Number of documents prepared by Bill = 2000
The amount he received = $474
a) The correct total pay that Bill should receive = 2000*25 = 50,000cents
Using the unitary method,
1 dollar = 100 cents
50,000 cents = 50000/100 = $500
b) The amount that his boss owes him = 500 - 474 = $26
Therefore using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.
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Please help meeeee with this
Answer:
30 mm
Step-by-step explanation:
just add the length of each side together
