The cost of having a car towed 14 miles is $103.
What is function ?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. Functions are often represented by a formula or rule that describes how to compute the output value from the input value.
The towing cost, C, can be expressed as a function of miles towed, x, using the given information as follows:
C(x) = 75 + 2x
where x is the number of miles towed.
To find the cost of towing a car 14 miles, we can substitute x = 14 into the function:
C(14) = 75 + 2(14)
= 75 + 28
= $103
Therefore, the cost of having a car towed 14 miles is $103.
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the explicit formula for this sequence: 2 6 18 54 162
Answer:
To find the explicit formula for this sequence, we need to determine the common ratio between successive terms. To do this, we can divide any term by the previous term. For example:
6 ÷ 2 = 3
18 ÷ 6 = 3
54 ÷ 18 = 3
162 ÷ 54 = 3
So the common ratio is 3.
Next, we can use the general form of a geometric sequence to find the explicit formula:
a(n) = a(1) * r^(n-1)
where a(n) is the nth term of the sequence, a(1) is the first term, r is the common ratio, and n is the position of the term we want to find.
In this sequence, a(1) = 2 and r = 3. So the explicit formula for this sequence is:
a(n) = 2 * 3^(n-1)
For example, if we want to find the 6th term, we can plug in n = 6:
a(6) = 2 * 3^(6-1) = 2 * 3^5 = 2 * 243 = 486
Therefore, the 6th term of the sequence is 486.
The following are infinite geometric series. For which infinite series could find the sum using a formula?
A) -2+6+(-18)+54+(-162)+...
B) 3+12+48+192+768+...
C) 1+2+4+8+16+...
D) 8+4+2+1+1/2+...
Answer:
D) 8 + 4 + 2 + 1 + 1/2 + ...
Step-by-step explanation:
The sum of an infinite geometric series can be found when the absolute value of the common ratio, r, is less than 1.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$,\quad $|r| < 1$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
To determine which of the given infinite geometric series can be summed using the formula, calculate the value of r for each series. To do this, divide a term by the previous term.
Given infinite geometric series:
-2 + 6 + (-18) + 54 + (-162) + ...[tex]\implies r=\dfrac{6}{-2}=-3[/tex]
As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.
Given infinite geometric series:
3 + 12 + 48 + 192 + 768 + ...[tex]\implies r=\dfrac{12}{3}=4[/tex]
As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.
Given infinite geometric series:
1 + 2 + 4 + 8 + 16 + ...[tex]\implies r=\dfrac{2}{1}=2[/tex]
As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.
Given infinite geometric series:
8 + 4 + 2 + 1 + 1/2 + ...[tex]\implies r=\dfrac{4}{8}=\dfrac{1}{2}[/tex]
As |r| < 1 the sum of the infinite series can be found using the formula.
Therefore, the infinite series for which the sum can be found by using the formula is:
D) 8 + 4 + 2 + 1 + 1/2 + ...answer correctly for brainly and 100 points
The missing reason for the following proof: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).
What is triangle?A triangle is a closed two-dimensional figure with three straight sides and three angles. It is formed by connecting three non-collinear points with straight lines. The sum of the interior angles of a triangle always equals 180 degrees, and the exterior angles of a triangle always add up to 360 degrees. Triangles are one of the fundamental shapes in geometry and have many different classifications based on their side lengths, angles, and other properties.
Here,
In geometry, CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a property that states that if two triangles are congruent, then their corresponding parts (angles and sides) are also congruent. In other words, if two triangles are the same shape and size, then all of their corresponding angles and sides are equal in measure. This property is often used in geometric proofs to show that two triangles are congruent by demonstrating that their corresponding parts are equal.
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For the breakfast buffet, Mr. Walker must equally divide 7 loaves of bread between five platters. How many loaves of bread are placed on each platter?
Answer:
the answer to ur question is: 1.4
PLEASE HELP DUE TODAY
The question: What theorem would you use to write proportion for this figure?
It's the same question for each problem.
7) through: (-4,-4), parallel to y=x-1
9) through: (-4,-4), parallel to y=-
y=-x-4
11) through: (5,-2), perp. to y=-x-5
13) through: (-2, 5), perp. to y = x + 2
8) through: (1,0), parallel to y=2x-1
10) through: (5.5), perp. to y
12) through: (3,-2), perp. to y ==
14) through: (-4, 0), perp. to y = -x-2
Answer:
14 is 45
Step-by-step explanation:
From 2014-2015 to 2024-2025, the number of students enrolled in an associate degree program is projected to increase by 21.5%. If the enrollment in associate degree programs in 2014-2015 is 6,500,000 , find the increase and the projected number of students in an associate degree program in 2024-2025.
in the number 423, 36/ the
underline 3 is blank times blank
Than the other 3.
Answer:
I'm sorry, but the question is unclear. Can you please provide more context or information so that I can understand what you are asking?
Simplify
to an expression involving a single trig function with no fractions.
If needed, enter squared trigonometric expressions using the following notation.
Example: Enter
as
The simplified form of csc²t/ [csc²(t) - 1] is sec²t
Trigonometric identities:Trigonometric identities are mathematical relationships between trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant. These identities are used to simplify trigonometric expressions and solve trigonometric equations.
To solve the given expression we used the following trigonometric identities
csc²(t) = 1/sin²(t)sin²(t) = 1 - cos²(t)sin²(t) + cos²(t) = 1Here we have
csc²t/ [csc²(t) - 1]
As we know csc θ = 1/sin θ
=> sinθ = 1/cscθ
Take csc² t as common from numerator and denominator
=> csc²t [1]/ csc²t [ 1 - (1/csc²t)]
=> 1/ 1 - (1/csc²t) [ csc²t will be canceled ]
=> 1/ 1 - sin²t
From trigonometric identities 1 - sin²t = cos²t
=> 1/ cos²t
= sec²t
Therefore,
The simplified form of csc²t/ [csc²(t) - 1] is sec²t
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Find the area, in square inches, of the composite figure.
A composite figure consisting of an isosceles right triangle, a rectangle, and an another isosceles triangle. The combined length of the right triangle and the rectangle is 25 inches. The length of only the rectangle is 14 inches. The base of the other isosceles triangle, which is the same as the width of the rectangle, is 2 inches plus 2 inches, and the height of the isosceles triangle is 3 inches.
The area of the composite figure is 122.5 square inches
How to find the area of the composite figure.Based on the problem statement, we have the following dimensions from the question
Isosceles right triangle: 11 inchesRectangle: 14 inches by 4 inchesAnother isosceles triangle; Base = 4 inches and Height = 3 inchsThe area of the composite figure is the sum of individual areas
So, we have
Area = Isosceles right triangle + Rectangle + Another isosceles triangle
By applying the formulas, we have
Area = 0.5 * 11 * 11 + 14 * 4 + 0.5 * 4 * 3
Evaluate
Area = 122.5
Hence the area is 122.5 sq inches
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What is the area of this triangle
The area of the triangle is 5/2 x sqrt(7) square units, or approximately 6.99 square units.
We need to know the triangle's base and height lengths in order to calculate its area.
Let's give the triangle's vertices the following names:
A is the bottom-left vertex.
B is the vertex at the bottom right.
C is the top vertex.
We can infer from the facts provided that the triangle's base measures AB, or 5 units.
We must draw a perpendicular line from the triangle's vertex C to its base AB in order to get the triangle's height. Let's give the intersection of the perpendicular line and the base the letter D.
Right triangle ACD with CD as the triangle's height now exists. The Pythagorean theorem can be used to determine CD's length:
[tex]AD^2 + CD^2 = AC^2[/tex]
We can determine that AC is 4 units and AD is 3 units based on the facts provided.
When we plug these figures into the formula, we get:
[tex]4^2 = 3^2 + CD^2[/tex]
Simplifying:
16 = 9 + [tex]CD^2[/tex]
[tex]CD^2[/tex] = 7
CD = √7
The triangle's height is therefore √7 units.
The area formula for triangles can now be used:
Area equals ([tex]\frac{1}{2}[/tex]) x base x height.
Adding the values we discovered:
Area equals ([tex]\frac{1}{2}[/tex]) x 5 sq (7)
Area = [tex]\frac{5}{2}[/tex] x sqrt (7)
Hence, the triangle has a surface area of [tex]\frac{5}{2}[/tex] x √7 square units, or roughly 6.99 square units.
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(05.03 MC)
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points)
Part B: Make tables to find the solution to 4x = 2x−2. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4x = 2x−2 graphically? (2 points)
(10 points)
Part A: The intersection of these two lines is (-1,-4). Since x=-1, this is also the solution to 4x=2x-2 as per the graph.
Part B: Table attached.
Part C: Graph attached.
What is a graph?Graphing a function involves tracing the curve on a coordinate plane that corresponds to the function. If the curve represents the function for the curve, then each point on the curve will satisfy the function equation. The graph below shows the linear function f(x) = -x+ 2 as an illustration.
In the question,
The expression 4x = 2x - 2 reduces to x = -1. This is true for all values of y, since y is not a factor in this expression.
The two other equations intersect at point (-1, -4). See the attached graph (Solutions2)
y = 4x
y = 2x−2
Mathematically, we can substitute the value of y from the first equation into the second:
y = 2x−2
(4x) = 2x−2
2x = -2
x = -1
The intersection of these two lines is (-1,-4). Since x=-1, this is also the solution to 4x=2x-2.
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Dylan earns money mowing lawns. The amount of money, in dollars, he earns varies as the number of lawns he mows. When he mows 6 lawns, he earns $72.
Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week,
300 customers visited the store.
What is the percentage change of the number of customers that visited the store in the first week to the number of customers that
visited the store in the second week?
OA. a 20% decrease
OB. a 16.7% increase
OC. a 20% increase
OD. a 16.7% decrease
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. shaded area is 0.1949
Answer: To find the indicated z-score for a shaded area of 0.1949 in the standard normal distribution, we need to use a z-table or a calculator with a built-in normal distribution function.
Using a z-table, we can find the z-score that corresponds to a cumulative area of 0.1949 in the standard normal distribution. The z-table gives us the area to the left of the z-score, so we need to look for the area closest to 0.1949 in the body of the table and then interpolate to find the exact z-score.
Looking at the z-table, we find that the area to the left of the z-score 0.88 is 0.8106, and the area to the left of the z-score 0.89 is 0.8159. Since 0.1949 is closer to 0.8106 than to 0.8159, we can estimate that the z-score corresponding to the area 0.1949 is approximately 0.88.
Therefore, the indicated z-score for a shaded area of 0.1949 in the standard normal distribution is approximately 0.88.
Step-by-step explanation:
I will mark you brainiest!
The shape above is NOT a polygon because:
A) There are two segments
B) The Shape includes a curve
C) There is one vertex
D) The shape is closed
express cos 0 as a ratio of given lengths of the right triangle shown
cos θ expressed as a ratio of given lengths of the right triangle is:
cos θ = 12/13
How to express cos θ as a ratio of given lengths of the right triangle?Trigonometry deals with the relationships between the sides and angles of triangles.
The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which are defined as follows:
Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.
Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
Thus, cos θ as a ratio of given lengths of the right triangle can be expressed as:
cos θ = 12/13 (cos = adjacent/hypotenuse)
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Complete Question
The attached image completes the question
Solve the rational equation symbolically, numerically, or graphically.
the solved equation will be x=7.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
2/X-5 - 4/ x+5 =2/ x²-25
[tex]\frac{(x+5)2-4(x-5)}{x^{2} -25}[/tex] = [tex]\frac{2}{x^{2} -25}[/tex]
2x-4x+10+20 = 2
-4x=-28
x=7
Hence, the solved equation will be x=7.
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9 x 1/5 = is the answer greater than or less than 9? why?
Step-by-step explanation:
help please I'll give brainliest
Answer:
k = 16.806404 and k = 95.174404
Step-by-step explanation:
To determine the value of k in which the graph touches, you set both equations equal to each other
4x + k = -x^2 +8x + 20
k = -x^2+4x+20
You can use the quadratic formula -b^2+-(sqrt(b^2-4(a)(c))) / 2a
You will get the values of x = -2.898 and 6.898 for your answers
My bad, I forgot to add also input the values of x in your equation and get k = 16.806404 and k = 95.174404
PLEASE HELP ILL GIVE BRAINLY!!
The expressiοn a² + b² = a + b is true when a = 1 and b = 1.
Define the term expressiοn?An expressiοn is a cοmbinatiοn οf variables, numbers, and mathematical οperatiοns that represents a quantity οr value. Expressiοns can be simple οr cοmplex, and they can invοlve a variety οf οperatiοns such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and radicals.
a. It is impοssible tο cοmbine the expressiοn √√3x + 2√3x intο a single term because the twο terms have different radical expressiοns. The first term has a dοuble square rοοt, while the secοnd term has a single square rοοt. These cannοt be cοmbined unless simplified first.
b. Ratiοnalizing the denοminatοr means tο eliminate any radical expressiοns frοm the denοminatοr οf a fractiοn by multiplying bοth the numeratοr and denοminatοr by a suitable expressiοn that will result in an integer οr ratiοnal denοminatοr.
c. Let a = 1 and b = 1, then a² + b² = 1² + 1² = 2, and a + b = 1 + 1 = 2. Therefοre, a² + b² = a + b is true when a = 1 and b = 1.
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PLEASE HELP ME ANSWER THIS QUESTION ASAP!!
Answer:
27.5
Step-by-step explanation:
What is μ (∠LMK)? thank you
Answer and Step-by-step explanation:
We can see that because Line K is acting as an Angle Bisector (a line that divides an angle into two angles of equal measures) on angle ∠LMJ, the angles ∠LMK and ∠JMK are equal to each other.
This allows us to solve for angle ∠LMK.
We do this by first setting the angles equal to each other.
10x - 22 = 2x + 66
Now, we want to isolate x by itself. We will subtract 2x from both sides of the equation, and then add 22 to both sides of the equation.
10x - 22 - 2x = 2x + 66 - 2x
8x - 22 = 66
8x - 22 + 22 = 66 + 22
8x = 88
Finally, we will divide both sides of the equation by 8.
8x ÷ 8 = 88 ÷ 8
x = 11
We aren't finished yet, as the question asks to find ∠LMK.
Plug 11 in for x into the equation 10x - 22.
10(11) - 22 =
110 - 22 =
= 88°
So, the measure of angle ∠LMK is 88°.
Have a good day!
need help with This Math
Answer:
Step-by-step explanation:
Firstly,
angles at the centre of a circle add to 360°. So
[tex](15x-1)+\angle ZVX +(8x-2)+(7x+15)+(3x+5)=360[/tex]
[tex]33x+17+\angle ZVX=360[/tex]
[tex]\angle ZVX=360-33x-17[/tex]
[tex]\angle ZVX=342-33x[/tex]
Secondly,
[tex]\angle YVU+ \angle UVW + \angle WVX =180[/tex]° (since YX is a diameter - angles on a
straight line sum to 180°)
[tex](3x+5)+(7x+15)+(8x-2)=180[/tex]
[tex]18x+18=180[/tex]
[tex]18x=162[/tex]
[tex]x=9[/tex]
Substitute [tex]x=9[/tex] into [tex]\angle ZVX=342-33x[/tex]:
[tex]\angle ZVX=342-33\times9=63[/tex]°
Solution: [tex]\angle ZVX=63[/tex]
The diagram shows a molecule of sulfur hexafluoride, the most potent greenhouse gas in the world. Name two different planes that contain line r.
Step-by-step explanation:
ADCF and DEFG
the third pane AECG is perpendicular to line r.
A triangle with vertices (4, 4), (4, 2), and (6, 3) is translated a distance of 4 units to the left. What are the new coordinates?
(0, 4), (0, 2), (2, 3)
(4, 0), (4, -2), (6, -1)
(4, 8), (4, 6), (6, 7)
(8, 4), (8, 2), (10, 3)
Option A. To translate a figure 4 units to the left, we need to subtract 4 from the x-coordinates of each vertex.
The original vertices are:
(4, 4), (4, 2), and (6, 3)
Subtracting 4 from the x-coordinates, we get the new vertices:
(0, 4), (0, 2), and (2, 3)
To understand how to translate a figure, it is helpful to visualize the original and new positions of the figure in a coordinate plane. In this case, the original triangle has vertices (4, 4), (4, 2), and (6, 3) as shown below:
(4,4)
/ \
/ \
(4,2)----- (6,3)
To translate this triangle 4 units to the left, we need to subtract 4 from the x-coordinates of each vertex. This will shift the entire triangle to the left by 4 units.
So, the new x-coordinates of the vertices become:
x-coordinate of (4, 4) - 4 = 0
x-coordinate of (4, 2) - 4 = 0
x-coordinate of (6, 3) - 4 = 2
The y-coordinates of the vertices remain the same.
Therefore, the new vertices of the triangle are:
(0, 4), (0, 2), and (2, 3)
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A triangle with vertices (4, 4), (4, 2), and (6, 3) is translated a distance of 4 units to the left. What are the new coordinates?
A. (0, 4), (0, 2), (2, 3)
B. (4, 0), (4, -2), (6, -1)
C. (4, 8), (4, 6), (6, 7)
D. (8, 4), (8, 2), (10, 3)
Consider the line y = -5/9x-2
9
Find the equation of the line that is parallel to this line and passes through the point (-9, -4).
Find the equation of the line that is perpendicular to this line and passes through the point (-9,-4
|
Plugging in the values, we get: [tex]y - (-4) = (9/5)(x - (-9))[/tex] simplifying and rearranging, we get the equation of the perpendicular line: [tex]y = (9/5)x + (16/5)[/tex]
What is the line that is perpendicular?To find the equation of a line that is parallel to [tex]y = (-5/9)x - 2,[/tex] we need to note that parallel lines have the same slope. The slope of [tex]y = (-5/9)x - 2[/tex] is -5/9, so the slope of the parallel line will also be -5/9.
We can use this information and the given point (-9, -4) to find the equation of the parallel line using the point-slope form of the equation of a line:
[tex]y - y1 = m(x - x1)[/tex]
where (x1, y1) is the given point and m is the slope of the line. Plugging in the values, we get:
[tex]y - (-4) = (-5/9)(x - (-9))[/tex]
Simplifying and rearranging, we get the equation of the parallel line:
[tex]y = (-5/9)x + (34/9)[/tex]
To find the equation of a line that is perpendicular to y = (-5/9)x - 2, we need to note that perpendicular lines have opposite reciprocal slopes. The slope of y = (-5/9)x - 2 is -5/9, so the slope of the perpendicular line will be 9/5 (the opposite reciprocal).
We can use this information and the given point (-9, -4) to find the equation of the perpendicular line using the point-slope form of the equation of a line:
[tex]y - y1 = m(x - x1)[/tex]
Therefore, where (x1, y1) is the given point and m is the slope of the line. Plugging in the values, we get: [tex]y - (-4) = (9/5)(x - (-9))[/tex] simplifying and rearranging, we get the equation of the perpendicular line: [tex]y = (9/5)x + (16/5)[/tex]
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solve by factoring. p^2-4=21. p= 1/4 or 21.
Therefore, the solutions to the equation [tex]p^{2} -4=21[/tex]are p = 3, -3, 7, and -7. Neither 1/4 nor 21 are solutions to this equation.
What is factor?In mathematics, a factor is a number or expression that divides another number or expression without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these numbers can all divide 12 evenly.
by the question.
We can solve this equation by first moving all the terms to one side of the equation:
[tex]p^{2}[/tex] - 4 = 21
[tex]p^{2}[/tex] = 25
Now, we can factor the left-hand side of the equation by using the difference of squares formula:
(p + 2) (p - 2) = 25
We can now solve for p by setting each factor equal to a possible value of the square root of 25:
p + 2 = 5 or p + 2 = -5
p - 2 = 5 or p - 2 = -5
Solving each of these equations, we get:
p = 3 or p = -7, p = 7 or p = -3
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an average bus speed between cape Town to east London was 108 km/h Due to the bad weather, the average speed on the trip back was 72 km/h. Determine how long the outward trip took if the return trip takes 12 hours
Answer:
Let's call the distance between Cape Town and East London "d".
We know that the average speed on the outward trip was 108 km/h, so the time it took to travel from Cape Town to East London can be calculated using the formula:
time = distance / speed
So the time it took on the outward trip can be expressed as:
time = d / 108
We also know that the average speed on the return trip was 72 km/h, and we're told that this trip took 12 hours. So we can use the same formula to find the distance between Cape Town and East London:
d = speed * time
d = 72 * 12
d = 864 km
Now we can use the formula for time again to find how long the outward trip took:
time = d / 108
time = 864 / 108
time = 8 hours
Therefore, the outward trip took 8 hours.
Step-by-step explanation:
Given: trap. SPQR with SP || QR ; MN is the median of the trap. m∠QRS = 120 ; m∠QPS = 135 ; SP = PQ = 12. Find: MN.
The value οf the median MN fοr the given trapezοid is 70.59 units.
What is the law οf sines?The law οf sines specifies hοw many sides there are in a triangle and hοw their individual sine angles are equal. The sine law, sine rule, and sine fοrmula are οther names fοr the sine law. The side οr unknοwn angle οf an οblique triangle is fοund using the law οf sine.
Any triangle that is nοt a right triangle is referred tο as an οblique triangle. At least twο angles and their cοrrespοnding side measurements shοuld be used at οnce fοr the sine law tο functiοn.
Given that, SPQR is a trapezοid with SP parallel tο QR,
Nοw, we knοw that MN is the average οf the lengths οf the bases SP and QR.
That is,
MN = (SP + QR) / 2.
Fοr the given values we have:
SP = PQ = 12, sο QR = 2MN - SP
Nοw, m∠QRS = 120 and m∠QPS = 135,
Thus,
m∠SPQ = 180 - 120 - 135 = -75.
Hοwever, angles cannοt be negative, sο we add 360 tο get 285 degrees.
Since SPQR is a trapezοid, we knοw that m∠SPQ = m∠QRN. Alsο, since MN is the median οf the trapezοid, it divides the trapezοid intο twο cοngruent triangles, sο m∠QMN = m∠RNM.
Using the law οf sines in triangle QMN tο find MN:
sin(m∠QMN) / MN = sin(m∠MQN) / QN.
Since QN = NR:
sin(m∠QMN) / MN = sin(m∠RNM) / NR.
sin(135) / MN = sin(285) / NR.
NR = sin(285) / sin(135) * MN.
2MN - SP = 2 * sin(285) / sin(135) * MN
2MN - 12 = 2.17MN
MN = 12 / 0.17 = 70.59
Hence, the value οf the median MN fοr the given trapezοid is 70.59 units.
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