p + q + 36 = 0 is the equation that is true. From this equation, we can say that p + q = -36.
If we substitute x = 1 in the given function, we get:
f(1) = [tex](1)^4 + 5(1)^3 + p(1)^2 + q(1) + 30[/tex]
= 1 + 5 + p + q + 30
= p + q + 36
We are given that f(1) = 0. Therefore, we have:
p + q + 36 = 0
This is the equation that is true. From this equation, we can say that p + q = -36.
Now, let's see why this is the case. When we substitute x = 1 in the given function and get f(1) = 0, it means that (1, 0) is a point on the graph of the function. This point lies on the x-axis, which means that the function intersects the x-axis at x = 1. Since the x-axis is the line y = 0, this means that f(x) = 0 when x = 1.
Using this information, we can write an equation in terms of p and q. If we substitute x = 1 in the given function and get f(1) = 0, it means that:
f(x) = [tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q))[/tex]
Therefore, we have:
[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = 0[/tex]
Since (1,0) is a point on the graph of the function, we know that x = 1 is a root of this equation. Therefore, we have:
[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = (x - 1)(x^2 + (7+p)x + (36-p-q))[/tex]
We know that (x - 1) is a factor of this equation, so we can use polynomial long division to divide the expression [tex](x^2 + (7+p)x + (36-p-q))[/tex] by (x - 1). The quotient will give us the other two roots of the equation. However, we do not need to find these roots to answer the question. All we need to know is that p + q = -36.
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Help pls
I need help asap i put the picture below
Answer:
d
Step-by-step explanation:
so b = 4
and the slope is rise over run = 5/2
Answer:
D) [tex]y=\frac{5}{2}x+4[/tex]
Step-by-step explanation:
The line equation of a line is:
[tex]y=mx+b[/tex] with m being the slope and b being the y-intercept.
We can see from the graph that the y-intercept is 4, as that's where the line intercepts the y-axis, and when x=0.
To find the slope, we first need to pick 2 points: (0,4) and (2,9).
The formula for slope is:
[tex]\frac{rise}{run}[/tex]
The rise is how many units you go up/down from one point to another. The run is how many units you go left/right from one point to another.
We can see that we go up 5 units and we go right 2 units. This means our slope is 5/2.
The completed line equation is:
[tex]y=\frac{5}{2}x+4[/tex], which means D is the correct option.
Hope this helps! :)
Pablo mixed
2
1
2
quarts of fruit juice with
1
gallon of seltzer. If each serving is
8
fluid ounces, how many servings did Pablo make?
A. 20
B. 26
C. 32
D. 36
The number of servings did Pablo make is (B) 26.
What is Unit conversion:Unit conversion is the process of converting a value expressed in one unit of measurement to another unit of measurement that represents the same quantity but is expressed in a different unit.
The given quantities are in different units, so we need to convert them to a common unit to determine the number of servings. For this, we need to convert quarts and gallons to fluid ounces.
Here we have
Pablo mixed 2 1/2 quarts of fruit juice with 1 gallon of seltzer.
Each serving is 8 fluid ounces
Let's first convert the quantities to the same units.
=> 1 gallon = 4 quarts
Total amount of liquid = 2 1/2 + 4 = 6 1/2 quarts
Now, let's find how many 8-ounce servings are in 6 1/2 quarts:
=> 1 quart = 32 fluid ounces
=> 6 1/2 quarts = 6.5 x 32 = 208 fluid ounces
Given that, 1 serving = 8 fluid ounces
Number of servings = 208/8 = 26
Therefore,
The number of servings did Pablo make is (B) 26.
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Complete Question:
Pablo mixed 2 1 /2 quarts of fruit juice with 1 gallon of seltzer. If each serving is 8 fluid ounces, how many servings did Pablo make?
A: 20 B: 26 C: 32 D: 36
In circle P, if mQR = 80 , and m QRT = 39 , find each measure
In circle P, if m(QR) = 80 , and m(QRT) = 39 , m(QPR) = 39 and m(PT) = 78
Based on the information given, we know that:
- m(QR) = 80 (this is the measure of arc QR)
- m(QRT) = 39 (this is the measure of angle QRT)
To find the other measures, we can use the following formulas:
- The measure of a central angle is equal to the measure of its intercepted arc
- The measure of an inscribed angle is half the measure of its intercepted arc
Using these formulas, we can find the measure of angle QPR and the measure of arc PT as follows:
- m(QPR) = m(QRT) = 39 (since angle QRT and angle QPR intercept the same arc QR)
- m(PT) = 2 * m(QRT) = 78 (since angle QRT and angle PQT intercept the same arc PT, and the measure of an inscribed angle is half the measure of its intercepted arc)
So the final answers are:
- m(QR) = 80
- m(QRT) = 39
- m(QPR) = 39
- m(PT) = 78
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Mr. jackers was transporting a giraffe from one zoo to another. what is a reasonable amount of the weight of his cargo?
a. 200 lbs.
b. 400 lbs.
c. 1 ton
d. 2 tons
The reasonable amount of weight of his cargo Mr. Jackers while transporting a giraffe from one zoo to another is 1 ton and 2 tons. Options C and D are correct.
To arrive at a reasonable estimate, we can consider the average weight of a giraffe, which ranges between 2,600 lbs and 4,250 lbs for adult males and females, respectively.
Therefore, a reasonable amount for the weight of Mr. Jackers' cargo would be between 2,600 lbs and 4,250 lbs, which translates to either 1 ton or 2 tons.
Thus, options c and d are the only reasonable answers, with d (2 tons) being the safer choice.
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Declan says, "To write an equivalent
fraction name for 5. I can write 5 as the
denominator and 1 as the numerator. "
Do you agree with Declan? Explain.
Declan's statement is technically correct, it is not a very helpful way to write an equivalent fraction for 5.
Declan's statement is mathematically correct, but it is not a useful way to write an equivalent fraction for 5 in most contexts.
In general, to write an equivalent fraction, we need to multiply or divide both the numerator and the denominator by the same nonzero number. This preserves the value of the fraction, but changes its form.
For example, to write an equivalent fraction for 5, we can multiply both the numerator and denominator by any nonzero number. Let's say we multiply both by 2:
5/1 = (5x2)/(1x2) = 10/2
So 10/2 is an equivalent fraction for 5.
However, if we follow Declan's approach and write 5 as the denominator and 1 as the numerator, we get:
5/1 = 1/5
This is indeed an equivalent fraction for 5, but it is not a particularly useful or common way to write an equivalent fraction. In general, we prefer to write equivalent fractions with a denominator that has some mathematical or practical significance, such as a power of 10 or a factor of the original denominator.
So while Declan's statement is technically correct, it is not a very helpful way to write an equivalent fraction for 5.
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Quadrilateral abcd is inscribed in this circle.
find the measure of angle a and angle b if
m&c = 121-and m&d=93°
а
d
b.
121°
с
The measure of angle a is 59 degrees and the measure of angle b is 87 degrees. Based on the information given, we know that angles a and b are opposite angles of the quadrilateral abcd,
So they are supplementary (their sum is 180 degrees).
We also know that angles c and d are opposite angles of the quadrilateral abcd, and they are given in the problem. Using the fact that angles on the same side of a chord are equal, we can say that angles a and d are equal, and angles b and c are equal.
Therefore, we can set up the following equation:
a + d = 180 (because they are supplementary)
d = 121
a = d (because they are opposite angles of the quadrilateral)
b = c (because they are opposite angles of the quadrilateral)
c + d = 180 (because they are supplementary)
c = 93
Substituting the known values, we get:
a + 121 = 180
a = 59
b + 93 = 180
b = 87
Therefore, the measure of angle a is 59 degrees and the measure of angle b is 87 degrees.
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Evaluate ∫∫∫ex dV where E is enclosed by the planes z = 0
and z = x + y + 5 and by the cylinders x^2 + y^2 = 4 and
x^2 + y^2 =9.
The E is enclosed by the planes z = 0 and z = x + y + 5
Why will E is enclosed by the planes z = 0?
The evaluate the triple integral ∫∫∫_E eˣ dV, where E is enclosed by the planes z = 0 and z = x + y + 5, and by the cylinders x² + y² = 4 and x² + y² = 9,
Follow these steps:
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a school has 475 students.If the ratio of girls to boys is 2:3, how many boys are there?
Answer:
2x + 3x = 475
= 5x = 475
= x = 475/5
= x = 95
Answer:
285 boys
Step-by-step explanation:
2 + 3 = 5
475/5=95
Girls: 2 x 95= 190
Boys: 3 x 95 = 285
Check
285 + 190= 475
A gym subscription runs several promotions. Customers can choose from the following offers.
Option A: 25% off an annual subscription of $308. 00
Option B: pay $29 per month
How much will a customer save by purchasing the annual subscription over paying per month?
a
$348
b
$231
c
$79
d
$117
A customer will save $117 by purchasing the annual subscription over paying per month. So the (d) $117 is the right answer.
To determine how much a customer will save by purchasing the annual subscription over paying per month, follow these steps:
Calculate the discounted annual subscription cost:
Option A: 25% off an annual subscription of $308.00
Discount = 25% of $308 = 0.25 * $308 = $77
Discounted Annual Subscription = $308 - $77 = $231
Calculate the total cost of the monthly subscription for one year:
Option B: Pay $29 per month
Total Monthly Subscription Cost = $29 * 12 months = $348
Calculate the savings:
Savings = Total Monthly Subscription Cost - Discounted Annual Subscription
Savings = $348 - $231 = $117
So, a customer will save $117 by purchasing the annual subscription over paying per month. Your answer is d. $117.
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An a frame house has a front facade measuring 30' across and 20' in height what is the area of the facade
The area of the facade measuring 30' across and 20' in height is 300 square feet.
The front facade of an A-frame house is a triangular shape, with a base of 30 feet and a height of 20 feet. To calculate the area of the facade, we need to use the formula for the area of a triangle, which is 1/2 times the base times the height = 1/2 * b * h, where b is the base and h is the height.
In this case, the base is 30 feet and the height is 20 feet, so we can plug those values into the formula:
Area = 1/2 x 30 x 20
Simplifying the multiplication, we get:
Area = 300 square feet
Therefore, the area of the front facade of the A-frame house is 300 square feet.
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Marshall and oliver went to an arcade where the machines took tokens. marshall played 10 games of skee ball and 8 games of pinball, using a total of 44 tokens. at the same time, oliver played 3 games of skee ball and 8 games of pinball, using up 30 tokens. how many tokens does each game require?
Each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.
Let the number of tokens required for each game of skee ball be x and for each game of pinball be y.
From the given information, we can form two equations:
10x + 8y = 44 ... (1)
3x + 8y = 30 ... (2)
Multiplying equation (2) by 3, we get:
9x + 24y = 90 ... (3)
Subtracting equation (1) from equation (3), we get:
- x + 16y = 46
Solving for x, we get:
x = 16y - 46
Substituting this value of x in equation (2), we get:
3(16y - 46) + 8y = 30
Simplifying and solving for y, we get:
y = 2
Substituting this value of y in equation (1), we get:
10x + 8(2) = 44
Solving for x, we get:
x = 2
Therefore, each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.
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determine the ordered pairs of....
[tex]6x - y > - 3[/tex]
and
[tex]4x + 3y < 4[/tex]
The ordered pairs of the system of inequalities are (1, 0) and (0, -5)
Determining the ordered pairs of the system of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
6x - y > -3
4x + 3y < 4
The above expression is a system of linear inequality
That implies that we graph the inequalites in the system on the same plane and write out ordered pairs from the region that represent the solution of the system
Next, we plot the graph
See attachment for the graph of the inequality
The ordered pairs are (1, 0), (0, -5) and other pairs
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Which axis is point 5 located on?
Point 5 is located on the x-axis (horizontal one)
In which axis is the point 5 located on?On a general coordinate axis we have two axes.
The vertical one is called the y-axis, and here we put the outputs.
The horizontal one is called the x-axis, here we put the inputs.
Here we can see that point 5 (P5) is located on the horizontal axis, then the correct option is the first one, x-axis.
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Solve the system of equations. 2x + 3y = 18 3x + y = 6 (9, 0) (3, 4) (1, 3) (0, 6)
X = 0 and Y = 6 are the answers to the equation system. The system's two equations are satisfied at the location (0, 6). Choice D
To solve the system of equations:
2x + 3y = 18
3x + y = 6
We can employ the substitution or elimination strategy. Let's solve this system via the process of elimination:
To make the coefficients of x in both equations equal, multiply the second equation by two:
2(3x + y) = 2(6)
6x + 2y = 12
Now we have the system of equations:
2x + 3y = 18
6x + 2y = 12
Next, by deducting the first equation from the second equation, we can remove the y term:
(6x + 2y) - (2x + 3y) = 12 - 18
6x + 2y - 2x - 3y = -6
4x - y = -6
4x - y = -6
y = 4x + 6
At this point, we can add this expression for y to one of the initial equations. Let's employ the first equation:
2x + 3(4x + 6) = 18
2x + 12x + 18 = 18
14x + 18 = 18
14x = 0
x = 0
Replacing x = 0 in the equation y = 4x + 6 now:
y = 4(0) + 6
y = 6
Thus, x = 0 and y = 6 are the answers to the system of equations. The system's two equations are satisfied at the location (0, 6). Basketball or baseball in option D is 5/6, or approximately 0.8333.
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Answer:
Option D, (0,6)
Step-by-step explanation:
took the test xx
_ x 10 = 3 1/2
what is in the blank help me pls
Answer:
x = 0.35
Step-by-step explanation:
We Know
x · 10 = 3 1/2
Find the missing number.
3 1/2 = 7/2 = 3.5
x · 10 = 3.5
x = 0.35
So, the answer is 0.35.
Find the mass of each object. (Round answers to two decimal places.)
A thin copper wire 3.75 feet long (starting at a = 0) with density function given by
p(t) = 5x^2 + 4x lb/ft.
The mass of the copper wire is approximately 131.77 lb.
To find the mass of the copper wire, we will first need to calculate its mass per unit length using the given density function[tex]p(t) = 5x^2 + 4x lb/ft,[/tex] and then integrate the function over the length of the wire.
Write down the given density function: [tex]p(t) = 5x^2 + 4x lb/ft[/tex]
2. Write down the limits of integration, which correspond to the length of the wire:
a = 0, b = 3.75 feett.
Set up the integral to find the mass of the wire:
Mass = ∫[p(t) dt] from a to b.
Plug in the density function and limits:
Mass = ∫[tex][5x^2 + 4x dx][/tex]from 0 to 3.75
Integrate the function: Mass = (5/3)x^3 + 2x^2 | from 0 to 3.75
Substitute the upper limit and then subtract the result of the lower limit:
Mass =[tex][(5/3)(3.75)^3 + 2(3.75)^2] - [(5/3)(0)^3 + 2(0)^2][/tex]
Perform the calculations and round to two decimal places:
Mass ≈ 131.77 lb.
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Pentagon
apothem = 7.3
side = 10.6
i need help immediately please help me show work
Answer:
Sure, I can help you with that!
To find the area of a regular pentagon, we can use the formula:
Area = (1/2) x apothem x perimeter
where apothem is the distance from the center of the pentagon to the midpoint of any side, and perimeter is the total length of all the sides.
So, to find the area of your pentagon, we can first calculate the perimeter:
Perimeter = 5 x side
Perimeter = 5 x 10.6
Perimeter = 53
Now, we can plug in the values for apothem and perimeter into the formula:
Area = (1/2) x apothem x perimeter
Area = (1/2) x 7.3 x 53
Area = 193.45
Therefore, the area of your pentagon is approximately 193.45 square units.
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Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother’s height minus sister’s height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (–0. 76, 4. 34). What was the sample mean difference from these 24 pairs of siblings?
–0. 76 inches
0 inches
1. 79 inches
4. 34 inches
The sample mean difference from these 24 pairs of siblings is 1.79 inches.
To find the sample mean difference from these 24 pairs of siblings, you can use the given 95% confidence interval for the mean difference in heights, which is (-0.76, 4.34).
The sample mean difference is the midpoint of the confidence interval. To calculate this, add the lower bound (-0.76) and the upper bound (4.34) of the confidence interval, and then divide by 2:
(-0.76 + 4.34) / 2 = 3.58 / 2 = 1.79 inches
So, the sample mean difference from these 24 pairs of siblings is 1.79 inches.
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1 ) If the supplement of an angle is 30 degrees more than the measure of the angle, what is the measure of the angle?
2) If the supplement of an angle is 12 degrees less than twice the measure of the angle, what is the measure of the angle?
a) If the supplement of an angle is 30 degrees more than the measure of the angle, the measure of the angle is 75 degrees.
b) If the supplement of an angle is 12 degrees less than twice the measure of the angle, the measure of the angle is 64 degrees.
a) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 30 degrees more than the measure of the angle. This can be written as:
180 - x = x + 30
Solving for x, we get:
2x = 150
x = 75
b) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 12 degrees less than twice the measure of the angle. This can be written as:
180 - x = 2x - 12
Solving for x, we get:
3x = 192
x = 64
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At Sugar Creek Middle School, there are two sizes of lockers for the students: one size for the sixth-grade and seventh-grade students and a larger size for the eighth-grade students. Both sizes of lockers are 5 feet tall and 1 foot wide. The lockers for the younger students each have a volume of 5 cubic feet, while the lockers for the eighth-grade students each have a volume of 7.5 cubic feet.
How much deeper are the lockers for the eighth-grade students than the lockers for the younger students?
21. The population of a small town is 15,000. If the population is growing
by 5% per year, how long will it take for the population to reach 25,000?
It will take the population 10.5 years to reach 25,000
How long will it take for the population to reach 25,000?From the question, we have the following parameters that can be used in our computation:
Inital population, a = 15000
Rate of increase, r = 5%
Using the above as a guide, we have the following:
The function of the situation is
f(x) = a * (1 + r)ˣ
So, we have
f(x) = 15000 * (1 + 5%)ˣ
When it reaches 25000, we have
15000 * (1 + 5%)ˣ = 25000
Divide both sides by 15000
(1 + 5%)ˣ = 1.67
Take the logarithm of both sides
x = log(1.67)/log(1 + 5%)
Evaluate
x = 10.5
Hence, the number of years is 10.5
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Determine the minimum and maximum value of the following trigonometric function.
f(x)=10sin(2/5x)+5
The minimum value of the function is -5 and the maximum value of the function is 15.
The minimum and maximum value of the given trigonometric function f(x)=10sin(2/5x)+5 can be determined by analyzing the amplitude and period of the sine function. The amplitude of the sine function is 10, which means that the maximum value of the function is 10+5=15 and the minimum value is -10+5=-5.
The period of the sine function is given by 2π/2/5=5π. This means that the function completes one full cycle every 5π units. To find the minimum and maximum values of the function, we need to evaluate it at the critical points of the function, which occur at intervals of 5π.
At x=0, the function has a value of 5+10sin(0)=15, which is the maximum value of the function. At x=5π/2, the function has a value of 5+10sin(2π/5)=5, which is the minimum value of the function.
At x=[tex]5π[/tex], the function has a value of 5+10sin(4π/5)=-5, which is the maximum value of the function. At x=15π/2, the function has a value of 5+10sin(6π/5) =5, which is the minimum value of the function.
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Peter eats 3 carrot sticks, with 1 cup of peanut butter, p, every day before lacrosse practice. he practices 4 days a week.
select all the equivalent expressions that represents how much peter eats before practice in one week.
To find out how much Peter eats in one week (which is 7 days), we need to multiply this expression by 7.
How much Peter eats before practice in one week?Peter eats 3 carrot sticks and 1 cup of peanut butter before lacrosse practice every day, so in one day he eats:
3 + p
To find out how much he eats in one week (which is 7 days), we need to multiply this expression by 7:
7(3 + p)
Distributing the 7, we get:
21 + 7p
So the equivalent expressions that represent how much Peter eats before practice in one week are:
3 + 4p + 3p
4(3 + p)
21 + 7p
7(3p + 1)
So the correct answers are:
4(3 + p)
21 + 7p
7(3p + 1)
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Tyler rides his bike from his house to his cousin's house. He bikes a total of 1.8 kilometers to get there and back. What is the distance, in meters, between Tyler's house and his cousin's house?
Answer:
Step-by-step explanation:
Total of rides from Tyler's house to Cousin's house and Cousin's house to Tyler's house = 1.8km = 1800m
So, the distance from Tyler's house to his cousin's house is
= 1800m ÷ 2 = 900m
11. a bird makes a dive off a cliff to catch a fish in a lake. the path of the dive follows a
parabolic curve of the given function f(x) = (x-7)2 - 1 where f(x) represents the height of
the bird in meters, and x represents the time in seconds. how far was the fish from the bird?
The fish has located a horizontal distance of 7 meters away from the cliff.
How to find the distance between the bird and the fish?
To find the distance between the bird and the fish, we need to find the horizontal distance traveled by the bird during the dive. We can do this by finding the x-coordinate of the vertex of the parabolic curve, which represents the highest point of the dive.
The vertex of the parabolic curve of the given function f(x) = (x-7)^2 - 1 is at the point (7, -1). This means that the highest point of the bird's dive is reached at 7 seconds, and the bird is at a height of -1 meters at this point.
To find the distance traveled by the bird during the dive, we need to find the horizontal distance between the bird's starting point (the cliff) and the highest point of the dive (the vertex). The distance is given by the horizontal coordinate of the vertex, which is 7 seconds.
Therefore, the fish has located a horizontal distance of 7 meters away from the cliff, assuming that the bird started the dive from the edge of the cliff.
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5. A ramp is to be built using a 20 foot long board and an 18 foot long board. To make die stable, the builders would like to add a third board to create a right triangle. How longed that board be, to the nearest hundredth of a foot?
The length of the third board the builders will add to create a right triangle, according to the Pythagorean Theorem is about 8.72 ft
What is the Pythagorean Theorem?Pythagorean Theorem is the relationship between the lengths of the three sides of a right triangle. The theorem states that the square of the length of the hypotenuse is equivalent to the sum of the square of the other two sides of the right triangle.
The specified dimensions of the ramp are;
Length of one side of the ramp = 20 ft
Length of the other side of the ramp = 18 ft
The shape of the triangle the builders would like to create = A right triangle
Let x represent the length of the third board, and let the 20 ft board represent the hypotenuse side. Pythagorean Theorem indicates that we get;
20² = 18² + x²
20² - 18² = x²
x² = 20² - 18² = 76
x = √(76) = 2·√(19) ≈ 8.72
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In circle m, secants pamd and pbc are drawn from point p such that mbc = 100 and mcd = 62°. which
of the following is the measure of p?
(1) 19
(2) 22
(3) 34
(4) 40
In the circle, the measure of p is 34 (option 3).
First, we know that angle MBC is an exterior angle to triangle PBC. Therefore, the measure of angle PBC is equal to the sum of angles MBC and MCB, which is 100 + (1/2)(angle MCP) = 100 + (1/2)(angle MQP).
Similarly, angle MCD is an exterior angle to triangle PCD. Therefore, the measure of angle PDC is equal to the sum of angles MCD and MDC, which is 62 + (1/2)(angle MPQ) = 62 + (1/2)(angle MQP).
Since angle PBC and angle PDC are both subtended by the same arc BC, they are equal. Therefore, we can set the expressions for these angles equal to each other and solve for angle MQP:
100 + (1/2)(angle MQP) = 62 + (1/2)(angle MQP)
38 = (1/2)(angle MQP)
angle MQP = 76 degrees
Finally, we can use the fact that angles MPQ and MQP form a linear pair, so they add up to 180 degrees. Therefore, angle MPQ is 180 - 76 = 104 degrees.
Since angle MPQ is an exterior angle to triangle PAB, we can use the exterior angle theorem to find the measure of angle P, as follows:
angle P = angle MPQ + angle PAB = 104 + 100 = 204 degrees
However, angles in a circle cannot be greater than 180 degrees, so we need to subtract 180 from angle P to get the actual measure of angle P:
angle P = 214 - 180 = 34 degrees
Therefore, the answer is option (3).
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If the price of a car is $5,900 and has a down payment of 15%, with a tax rate of 8.5%, how much will the amount of the loan need to be for?
A shipping company uses baggage tags with 3-letter city codes. The first and third letters of each code are always consonants and the middle letter is always a vowel (CVC). The English language uses 21 consonants and 5 vowels. How many different combinations of tag codes are possible? I will give brainliest to the best
(A) 105
(B)441
(C) 1,638
(D)2,205
The correct answer is (D) 2,205.
How to calculate the number of different combinations of baggage tag codes for a shipping company?To calculate the number of different combinations of tag codes, we need to consider the possible options for each position in the code.
For the first and third positions (consonants), we have 21 options for each position since there are 21 consonants in the English language.
For the middle position (vowel), we have 5 options since there are 5 vowels in the English language.
Therefore, the total number of different combinations is calculated by multiplying the number of options for each position:
21 (consonant options) * 5 (vowel options) * 21 (consonant options) = 2,205
Therefore, the correct answer is (D) 2,205.
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Find the y-component of this
vector:
42.2°
101 m
Remember, angles are measured from
the +x axis.
Y-component of the vector as shown in the diagram is 67.84 m in the direction of the negative y-axis.
What is a vector?Vector is a quantity that has both magnitude and direction.
Examples a vectors are
VelocityAccelerationDisplacementForceWeightMoment. Etc.To find the Y-component of the vector, we use the formula below.
Formula:
Y = dsinα................. Equation 1Where:
Y = Y-component of the vectord = Distance of the vector along the x-y planeα = Angle of the vector to the x-axisFrom the question,
Given:
d = 101 mα = (180+42.2) = 222.2°Substitute these values into equation 1
Y = 101sin222.2°Y = 67.84 mHence, the y component is 67.84 m.
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