David and Daniel were given $12 each in the beginning as the given condition.
What are conditions?
A condition that must be met in order for the given statement or theorem to hold. also known as a problem.A necessary condition is one that must exist in order for the given statement to be true (if satisfied it maybe true as there maybe more than one necessary conditions). On the other hand, a sufficient condition is one that, even if it is satisfied, does not automatically imply that the proposition is true.Let david and daniel were given = $x each as per statement.
at the end david had = 2x
and daniel had= x+12
Condition is given that : in the end, the boys still have the same amount of money.
Therefore, equating both what David and Daniel had
2x=x+12
x=12
David and Daniel were given $12 each in the beginning as the given condition.
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Kylie gets an email
account for 7
months. She puts in
$681 in her email
account and she
earns 55% each year
How much interest
will
she earn?
Kylie gets an interest of $214.48.
What do you mean by interest?
In the fields of finance and economics, interest is the payment of a sum over and above the principle amount to a lender or depositor by a borrower or deposit-taking financial institution at a set rate. Interest is not the same as a charge that the borrower could pay to the lender or another entity. Additionally, it differs from a dividend, which is a payment made to shareholders from a company's profit or reserve, but not at a set rate predetermined in advance, but rather on a pro rata basis as a portion of the rewards received by risk-taking business owners when revenue earned exceeds all costs. In contrast to profit, which is obtained by the owner of an asset, investment, or business, interest is paid to the lender.
Interest earned by Kylie = (55x7)/(100x12) x 681
= 218.48
Hence, Kylie gets an interest of $218.48.
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A biker rode 3.75 miles in 0.3 hrs
A) how fast is she going?
B) how long will it take her to go 4.5ml?
bike ride is 3.75 miles, or 4.5ml is
3.75/.3 (or 4.5/x.36) (or x 1).
Timing is 0.3 hours.
Speed = Distance / Time Speed = 3.75 x 0.3 = 12.5 mph.
2) Speed is 12.5 mph, and the distance is 4.5 miles.
Time = Distance * Speed.
Time = 4.5 * 12. 5 = 0.36 hours.
It takes 0.36 hours to travel 4.5 miles.
How is the speed per hour determined?
Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed. The units in this example will be meters per second (m/s), since the distance is measured in meters (m) and the time is measured in seconds (s).
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If f(n) = n 2 - n, then f(-4) is _____.
first f(-4)=-4(2)-(-4)
=-8+4
=-4
answer :-4
B is between A and C. C is the midpoint of BD. D is between C and E.
AB=6x+5, BC=3x+1, DE=7x+3, AE =12x+31 Find AD.
C is the midpoint of BD, Therefore, BC = CD
Now, AD = AB + BC + CD = (6x +5) + (3x + 1) + (3x + 1) = 12x + 7 .... eqn 1
Also, AD = AE - DE = (12x + 31) - (7x + 3) = 5x + 28 ....... eqn 2
From Eqn 1 and Eqn 2,
12x + 7 = 5x + 28
⇒ 12x - 5x = 28 - 7
⇒ 7x = 21
⇒ x = 21/7
⇒ x = 3
So, AD = 12x + 7 = 12(3) + 7 = 36+7
⇒ AD = 43 units
What is a Line segment?A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length. Half-open line segments contain exactly one of the endpoints, while closed-line segments have both of the endpoints. Open line segments do not contain either of the endpoints. A line drawn above the symbols for the two endpoints is frequently used in geometry to indicate a line segment.The sides of a triangle or a square are examples of line segments. A line segment is either an edge (of that polygon or polyhedron) if its endpoints are nearby vertices, or a diagonal more broadly when both of its end points are vertices of a polygon or polyhedron. A line segment is referred to as a chord when both of its endpoints are located on a curve, like a circle (of that curve).To learn more about the Line segment, refer to:
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State which property you would use to solve 8X = 56
X = 7 divid both sides
8x = 56
8x/8 and 56/8 .
A shape has only three angles, and only one of those angles measures 90 degrees. What is the name of the shape?
Answer:
A right Triangle
Step-by-step explanation:
A right triangle has 3 angles and one of those angles measures 90 degrees.
Can someone let me know if I’m right?
Answer:
d
Step-by-step explanation:
using the tangent ratio in the right triangle
tan61° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{3.8}[/tex] ( multiply both sides by 3.8 )
3.8 × tan61° = x , then
x ≈ 6.9 cm ( to the nearest tenth )
Mrs. Shaughnessy’s science class and Mr. Ruth’s social studies class are going on two separate field trips. They have the same budget for their trips. Mrs. Shaughnessy’s class has 30 students, and they are taking a bus to a planetarium. Mr. Ruth’s class of 20 students is taking the subway to a museum. Admission to the planetarium is 12 the cost of admission to the museum, as shown in the table. What is the cost of admission per student to the museum?
The cost of admission per student is given as 10 dollars to the museum
How to solve for the costWe have the following details that we would have to solve this problem with.
The number of people in this Mrs Shaughnessy’s class is 30 students
The number of persons in Mr Ruth's class is 20 students
The admission that is made to the planetarium is given as 12
we would have this equation
30 * 1/2x + 3 x 30
= 15x + 90
For the next equation we would have
20 x x + 2 x 20
= 20x + 40
We have to make the two equations to be equal
15x + 90 = 20x + 40
take the like terms
15x - 20x = 40 - 90
-5x = -50
divide through by -5 to get the value of x
x = -50 / -5
x = 10
Therefore the cost of admission per student would be 10 dollars
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Simplify. (5x² + 2x - 5) (3x² + 3x + 1)
Answer: 15[tex]x^{4}[/tex]+21[tex]x^{3}[/tex]-4[tex]x^{2}[/tex]-13[tex]x[/tex]-5
Step-by-step explanation:
(5x² + 2x - 5) (3x² + 3x + 1) times the two brackets together.
15[tex]x^{4}[/tex] + 15[tex]x^{3}[/tex]+ 5[tex]x^{2}[/tex]+6[tex]x^{3[/tex]+6[tex]x^{2}[/tex]+2[tex]x[/tex]-15[tex]x^{2}[/tex]-15[tex]x[/tex]-5 simplified =
15[tex]x^{4}[/tex]+21[tex]x^{3}[/tex]-4[tex]x^{2}[/tex]-13[tex]x[/tex]-5
On Monday Harold picked up six donuts and two large coffees for the office staff. He paid $5.80. On Tuesday, Melinda picked up four donuts and 5 large coffees for the office staff. She paid $7.02. What is the cost of one donut? What is the cost of one large coffee?
Cost of tjhe donut: D
Cost of the large coffee: C
On Monday Harold picked up six donuts and two large coffees for the office staff, he paid $5.80:
[tex]6D+2C=5.80[/tex]On Tuesday, Melinda picked up four donuts and 5 large coffees for the office staff. She paid $7.02:
[tex]4D+5C=7.02[/tex]Use the next system of linear equations to find the value of D and C:
[tex]\begin{gathered} 6D+2C=5.80 \\ 4D+5C=7.02 \end{gathered}[/tex]1. Solve D in the first equation:
[tex]\begin{gathered} \text{Subtract 2C in both sides of the equation:} \\ 6D+2C-2C=5.80-2C \\ 6D=5.80-2C \\ \\ \text{Divide both sides of the equation into 6:} \\ \frac{6}{6}D=\frac{5.80}{6}-\frac{2}{6}C \\ \\ D=\frac{5.80}{6}-\frac{1}{3}C \end{gathered}[/tex]2. Substitute the D in the second equation by the equation you get in step 1:
[tex]4(\frac{5.80}{6}-\frac{1}{3}C)+5C=7.02[/tex]3. Solve C:
[tex]\begin{gathered} \frac{23.2}{6}-\frac{4}{3}C+5C=7.02 \\ \\ \frac{-4C+15C}{3}=7.02-\frac{23.2}{6} \\ \\ \frac{11}{3}C=\frac{42.12-23.2}{6} \\ \\ \frac{11}{3}C=\frac{18.92}{6} \\ \\ C=\frac{3}{11}\cdot\frac{18.92}{6} \\ \\ C=\frac{56.76}{66} \\ \\ C=0.86 \end{gathered}[/tex]4. Use the value of C=0.86 to find D;
[tex]\begin{gathered} D=\frac{5.80}{6}-\frac{1}{3}C \\ \\ D=\frac{5.80}{6}-\frac{1}{3}(0.86) \\ \\ D=\frac{5.80}{6}-\frac{0.86}{3} \\ \\ D=\frac{17.4-5.16}{18} \\ \\ D=\frac{12.24}{18} \\ \\ D=0.68 \end{gathered}[/tex]The solution fot the system is:
[tex]\begin{gathered} C=0.86 \\ D=0.68 \end{gathered}[/tex]The cost of one dount is $0.68The cost of one large coffee is $0.8625x = 3 (1 + 8x) + 2
x=7
x = 5
x=2
x = 11
In the given equation 25x = 3 (1 + 8x) + 2, the value of x is found to be x = 5 by solving the equation.
What exactly is an equation?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.What are the three kinds of equations?Linear equations are classified into three types: point-slope, standard, and slope-intercept.
The given equation is :
25x = 3 (1 + 8x) + 2
On solving the equation for x we get,
25x = 3 + 24x + 2
25x - 24x = 5
x = 5
Therefore, the value of x in the given equation 25x = 3 (1 + 8x) + 2 is found to be x = 5.
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15. A copying service charges a uniform rate for the first one hundred copies or less and a fee
for each additional copy. Nancy Taylor paid $7.00 to make 200 copies and Rosie Barbi paid
$9.20 to make 310 copies.
c. What is the cost of the first one hundred copies?
d. What is the cost of each additional copy?
The cost of the first hundred copies is $5
The cost of each additional copy is $0.02
What are the costs?The first step is to form a system of equation using the information that is provided in the question:
100a + [(200 - 100)b] = 7
100a + 100b = 7 equation 1
100a + [(310 - 100)b] = 9.20
100a + 210b = 9.2 equation 2
Where:
a = cost of each of the first hundred copiesb = cost of the additional copiesThe two equations formed above would be solved using the elimination method.
Subtract equation 1 from equation 2
110b = 2.2
Divide both sides of the equation by 110: b = 2.2 / 110
b = 0.02
Substitute for b in equation 1:
100a + 100(0.02) = 7
100a + 2 = 7
Combine similar terms: 100a = 7 - 2
Add similar terms: 100a = 5
Divide both sides of the equation by 100 : a = 5 / 100
a = 0.05
Cost of the first hundred copies = $0.05 x 100 = $5
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tickets for a raffle cost $ 5. there were 832 tickets sold. one ticket will be randomly selected as the winner, and that person wins $ 1600 and also the person is given back the cost of the ticket. for someone who buys a ticket, what is the expected value (the mean of the distribution)?
The most appropriate choice for expectation will be given by-
Expected value for someone who buys the ticket = $[tex](-1591.2)[/tex]
What is expectation?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Suppose x is a random variable with the probability function f(x). suppose
[tex]x_1. x_2,........,x_n[/tex] are the values corrosponding to the actual occurance of the event and [tex]p_1, p_2.,,,, p_n[/tex] be the corrosponding probabilities.
Expectation is given by the formula [tex]p_1x_1+p_2x_2+...+p_nx_n[/tex]
Here,
Total number of tickets = 832
Number of prized tickets = 1
Probability of winning a ticket = [tex]\frac{1}{832}[/tex]
Probability of losing a ticket = [tex]\frac{831}{832}[/tex]
Gain of winning = $(1600 - 5) = $1595
Loss of losing = $(5 - 1600) = -$1595
Expected value for someone who buys the ticket
[tex]1595 \times \frac{1}{832} + (-1595)\times \frac{831}{832}[/tex]
[tex]1595\times(\frac{1-831}{832})\\-1595\times \frac{830}{832}\\[/tex]
$[tex](-1591.2)[/tex]
Expected value for someone who buys the ticket = $[tex](-1591.2)[/tex]
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Can anyone give me a hand?
Answer:
Step-by-step explanation:
I tried to put my hand through the computer but it didn't work! Lol
Anyways,
m<WZY= 70 degrees
35+35= 70
Answer:
70
Step-by-step explanation:
Angle WZX = 35
As ZX is a bisector, it cuts it down the middle and splits it in half. This means that angle WZX is half of the original angle, WZY.
35 * 2 = 70.
Which expression has a value of -10 when p=25 and q = 10? OA) 3√p-q+5 OB) 3√√p-q)+5 OC) (3√ √p)-q+5 OD) 3√√p(q+5)
Answer:
Answer B
Step-by-step explanation:
B is:
[tex]3 (\sqrt{25} - 10) + 5 \\ 3(5 - 10) + 5 \\ 3 ( - 5) + 5 \\ - 15 + 5 = - 10[/tex]
fabiana opened a savings account with $14,200 that earns 1.2% simple interest annually. after how many years will the balance of the account be $15,478 ? round to the nearest tenth if necessary.
After 7.5 years will the balance of the account be $15,478.
Given:
fabiana opened a savings account with $14,200 that earns 1.2% simple interest annually.
here A = 15478 , p = 14,200 , r = 1.2%
Simple interest formula:
A = p(1 + rt)
15478 = 14,200(1 + 1.2%t)
15478 = 14,200 + 14,200(0.012t)
1278 = 170.4t
t = 1278/170.4
t = 7.5 years
Therefore after 7.5 years will the balance of the account be $15,478.
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Angela is building a fence for a circular playground, with a radius of 7 feet. How much fence will Angela need for the playground?
Given:
Circular playground with radius=7 feet
To find:
Fence for the playground
Solution:
To find the fence required for the circular playground, we will have to find the circumference of the ground.
Circumference =2πR ( where R is the radius of the circle)
= 2*3.14*7
= 44 feet
Therefore, the fence required is 44 feet.
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Use the drop-down menus to complete each equation so the statement about its solution is true.
You have not provided the contents of any of the drop-down menus, so we cannot say for certain what the answers should be--except in the case of "infinitely many solutions.
For no solution,2x + 9 + 3x + x = 6x
For one solution,2x + 9 + 3x + x = 15
For infinitely many solutions,2x + 9 + 3x + x = 6x + 9
Based on the given conditions,
(1) No solutions :
There will be no solutions when the left side is inconsistent with the right side:
2x + 9 + 3x + x = _ x + _
We can sum of difference,
6x + 9 = 6x
Subtract 6x from both sides,
6x - 6x = -9
9 = 0
9 = 0 which is absurd and hence the equation has no solution.
(2) One solutions :
There will be one solution when the left side and right side are not inconsistent and not the same.
2x + 9 + 3x + x = 15
6x + 9 = 15
Subtract 9 from both sides.
6x = 6
Divide both sides by 6.
x = 1 and this is the only solution.
(3) Infinity solutions :
There will be an infinite number of solutions when the equation is true for any value of x. This will be the case when the left side and right side are identical.
2x + 9 + 3x + x = 6x + 9
6x + 9 = 6x + 9
Subtract 6x from both sides,
9 = 9, both sides are balanced which means, the equation has infinitely many solutions.
Therefore,
For no solution,2x + 9 + 3x + x = 6x
For one solution,2x + 9 + 3x + x = 15
For infinitely many solutions,2x + 9 + 3x + x = 6x + 9
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A formula for converting degrees Fahrenheit (F) to degrees Celsius(C) is given by the formula C = 5/9(F -32). Solve the formula for F in terms of C.
Answer:
F=(9C/5)+32
Step-by-step explanation:
In the image
Complete the equation of the line through (-1,6) and (7,2)
The equation of the straight line is 2y - x +3 = 0 .
A straight line's general equation is y = mx + c, wherein m denotes the line's slope and c its y-intercept.
It is the geometry-related straight line equation that is employed the most frequently. A straight line's equation can be expressed in a variety of ways, including point-slope form, slope-intercept form, generic form, standard form, etc. A solid line is a two-dimensional geometric object that can be stretched to infinity on both ends.Let us calculate the slope of the line:
slope = (2-6)/(7-(-1))
m= 1/2
Equation of the line =
y - 2 = 1/2 (x-7)
or, 2y -4 = x - 7
or, 2y - x +3 = 0
Therefore the equation of the line is 2y - x +3 = 0.
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Someone please help me
Using relations in a right triangle, it is found that:
1. Angelica's mistake is stating that we can find the length of AB, as we can only find the simplified length with the ratio, not the actual length.
2. Graziella mistake is stating that since we don't know the sides we cannot find the ratios.
3. The measures are as follows: sin(A) = 3/5, cos(A) = 4/5.
What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
Sine: opposite side/hypotenuse.Cosine: adjacent side/hypotenuse.Tangent: opposite side/adjacent side.In this problem, we have that the tangent of angle A is of 3/4, hence the lengths are given as follows:
AC = 4.BC = 3.Applying the Pythagorean Theorem, the hypotenuse AB is given as follows:
x² = 3² + 4²
x² = 9 + 16
x² = 25
x = 5.
Then the sine and the cosine of A are given as follows:
sin(A) = 3/5.cos(A) = 4/5.This is a procedure in which we can find the smallest possible length of the hypotenuse, not the actual length, which is Angelica's mistake.
Even without knowing the actual length, we could find the ratios for the sine and for the cosine, which is Graziela's mistake.
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Find the coordinates of G if F(1, 3.5) is the midpoint of GJ and J has coordinates
(6,-2).
The coordinates of g are (-4, 9).
What are coordinates?A pair of numbers that represent a point's position on a coordinate plane using the horizontal and vertical distances between the two references. Usually represented by the pair of x and y values (x,y). A coordinate system can be used to determine a point's exact location on the globe. A coordinate is a pair of numbers that describes the location of a point in a coordinate system. The distance between the point and the origin, which is a fixed point of reference, is represented by each of these values.So, the midpoint is given as (1, 3.5).
The coordinates of J are (6, -2).The midpoint is between the letters G and J.Let, G's coordinates are (x, y)Then,
(1, 3.5) = [(6 + x)/2, (-2 + y)/2]So,
1 = (6 + x)/22 = 6 + xx = 2 - 6x = -4And,
3.5 = (-2 + y)/23.5 × 2 = -2 + y7 = -2 + yy = 7 + 2y = 9Therefore, the coordinates of g are (-4, 9).
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How long can someone shower to use only 10 gallons of water?
Answer:
4 minutes
Step-by-step explanation:
A standard showerhead uses 2.5 gallons a minute, or 25 gallons for 10 minutes, therefore 10/2.5 = 4.
if a television screen with a length-to-height ratio of 16:9 has an area of 576 square inches, what is its perimeter?
The perimeter of television is = 100 inches
What is mensuration ?The study of measuring geometric shapes and their qualities such as length, volume, shape, surface area, lateral surface area, and so on is known as mensuration. Mensuration will be covered in fundamental mathematics.
Calculationlet the length be 16x and width be 9x
area given = 576 sq. inches
16x * 9 x = 576
144 [tex]x^{2}[/tex] = 576
x = 24/12
x = 2
length = 32
width = 18
perimeter = (32 + 18)*2 =100 inches
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A parasail is $\frac{3}{100}$
mile above the water. After 5 minutes, the parasail is $\frac{1}{50}$
mile above the water. Find the change in height of the parasail.
The change is height is
mile.
The change in height of the parasail = 1/100.
What is height?Height of defined as the measurement that is taken for an object which starts from its base to the topmost point. This is usually measured in meters.
From the question,
The height of the parasail above the water level= 3/100
The height of the parasail above the water level after 5 minutes= 1/50
The change in height of the parasail is determined by finding the difference between the two heights.
That is, = 3/100 - 1/50
= 0.03- 0.02 = 0.01
When changed to fraction is = 1/100
Therefore, the change in height after 5 minutes is = 1/100
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Delvin is practicing free throw shots. After a jump, Delvin releases the basketball from a height of 8 feet (ft) above the ground. When the ball is 2 ft horizontally from Delvin, it is 11 ft in the air. The ball then passes through the basket, which is 10 ft above the ground and 15 ft horizontally from Delvin. What is the maximum height that the basketball reaches in its path? You can assume that the ball travels in a parabolic arc, as shown in the figure.
The maximum height that the basketball reaches in its path is 8.48ft
What is Parabola?A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Then the path of the ball may be modeled by the parabola
y = (-16x^2/0.434v^2)+1.15x+8
Let x = 15
y = 10
Then, Substituting the value of x and y
10 = (-16(15)^2/0.434v^2)+1.15(15)+8
10 = (-16(225)/0.434v^2)+17.25+8
10 = (-3600/0.434v^2) + 25.25
Subtracting 25.25 both side we get
-15.25 = (-3600/0.434v^2)
Multiplying v^2 both side we get
-15.25v^2 = -3600/0.434
-15.25v^2 = -8294.93
Dividing -15.25 both side we get
v^2 = -8294.93/-15.25
v^2 = 543.93
v = [tex]\sqrt{543.93}[/tex]
v = 23.32ft/sec
To find the maximum height we use
max = -b/2a
Lets find out a and be by
y = (-16x^2/0.434(23.32)^2)+1.15x+8
y = 0.06779 + 1.15x + 8
where, a = 0.06779 and b = 1.15
Substituting the value
max = -1.15/2(0.06779)
max = 8.48 ft
Hence, The maximum height that the basketball reaches in its path is 8.48ft
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8 = 8 (v - 5) is the solution 6 or -10 or -1 or 2 or is none of them the solution
Answer:
solution is v=6
Step-by-step explanation:
8=8(v-5)
1. expand the brackets
8=8v-40
2. get the v on one side so we +40 on each side
48=8v
3. divide each side by 8 as we want the value of v not 8v
6=v
4. Therefore your final answer is v=6 (solution is 6)
What is the missing length?
Please answer quick!
The missing length of the right triangle is found to be
What is termed as the right triangle?A right triangle is one where one of the interior angles is 90°. The hypotenuse is the longest side of a right triangle as well as the side opposite the right angle, while the height and base are the two arms of the right angle.Right Triangle CharacteristicsIn a right triangle, the right angle is the largest.The longest side is the hypotenuse, which is the side opposite this same right angle.A right triangle cannot have any obtuse angles.For the given question;
The area of the right triangle is 112.7 cm².
The base of the right triangle is 16.1 cm.
The formula for finding the area of the triangle is-
Area = ¹/₂ base × height
Height = 2 area/ base
Put the values,
Height 'P' = 2 × 112.7 / 16.1
Height 'P' = 14
Thus, the missing side 'P' of the right triangle is found as 14 cm.
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F(x)=7x-4 and f(x)=17 find x
Answer:
x = 3
Step-by-step explanation:
We are given an equation in function notation and asked to solve for x. We can do this by isolating the variable.
Solving for x
First, substitute 17 into the equation for f(x).
17 = 7x - 4Now, we can isolate the x-variable by adding 4 to both sides.
21 = 7xThen, divide both sides by 7.
3 = xThis means when f(x) = 17, x = 3.
Checking the Answer
Now that we have solved for x, we can check the answer we got. Plug 3 into the original equation for x and see if the equation remains true.
17 = 7(3) - 417 = 17Since 17 = 17 is a true statement, the answer x = 3 must be correct.
Keandra is taking a trip to visit her extended family and makes a stop somewhere during her trip. The distance between Cincinnati, where Keandra started, and Dayton, where Keandra made the stop is 54 miles. The distance between Dayton and Toledo, where Keandra’s family lives is 150.2 miles. How far did Keandra travel on her trip? Round to the correct number of significant figures.
Keandra travelled a total distance of 204.2 miles on her trip
Distance between Cincinnati and Dayton = 54 miles
Distance between Dayton and Toledo = 150.2 miles
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language (e.g. "two counties over"). For instance: - My office and house are 3 kilometres apart.
Total distance travelled by Keandra from Cincinnati to Toledo = Distance between Cincinnati and Dayton + Distance between Dayton and Toledo
= 54 + 150.2
= 204.2 miles
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