A stunt man wants to drive a car off a ramp at an angle of 35∘ from the ground. He already has a ramp with an angle of 15∘. He plans to add a second ramp on top to increase the angle to 35∘. What angle measure does the second ramp need to have?
The second ramp needs to have an angle of 20° from the ground to achieve the overall angle of 35° for the car to drive off smoothly and reach the desired height.
Here,
To find the angle measure the second ramp needs to have, we can use the concept of angles of elevation and depression.
When the car drives off the first ramp, it will be going at an angle of 15° from the ground, and the angle of elevation from the ground to the car will also be 15°.
This is because the angle of elevation is the angle between the horizontal line and the line of sight from the ground to an object above the ground.
Now, when the car reaches the top of the first ramp, it will be at the same level as the second ramp.
At this point, the car needs to continue its ascent with an additional angle of 20° (35° - 15°) to reach the desired angle of 35° from the ground.
So, the second ramp needs to have an angle of 20° from the ground to achieve the overall angle of 35° for the car to drive off smoothly and reach the desired height.
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Quadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that ∠CFE and ∠CDE are supplementary?
Quadrilateral CDEF is inscribed in circle A.
Quadrilateral CDEF is inscribed in circle A, so m arc CDE+ m arc CFE= 360°. ∠CFE and ∠CDE are _________________, which means that their measures are one half the measure of their intercepted arcs. So, m arc CDE= 2 ⋅ m∠CFE and arc CFE= 2 ⋅ m∠CDE. Using the _________________, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.
inscribed angles; substitution property of equality
central angles; substitution property of equality
inscribed angles; addition property of equality
central angles; addition property of equality
Answer:
Inscribed angles, substitution property of equality
Step-by-step explanation:
We know it cant be Central angles because its a quadrilateral so that's 2 answers out. Then you have to substitute each value to end up with 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°, it doesnt make sense to add to both sides so the answer is Inscribed angles and substitution property of equality.
Plus i took the test and its right.
Angles to be proven as supplementary angles are known as inscribed
angles, and they are used as the substitute to known angles.
Response:
Inscribed angles; substitution property of equalityWhich method can be used to determine the correct option to complete the statement?The given information are;
Quadrilateral CDEF is inscribed in circle A
The completed statement is presented as follows;
Quadrilateral CDEF is inscribed in circle A, so [tex]m \widehat{CDE}[/tex] + [tex]m \widehat{CFE}[/tex] = 360°, ∠CFE and ∠CDE are inscribed angles, which means that their measures are [tex]\dfrac{1}{2}[/tex] the measures of the intercepted arcs. So [tex]m \widehat{CDE}[/tex] = 2·m∠CFE and [tex]m \widehat{CFE}[/tex] = 2·m∠CDE. Using the substitution property of equality, 2·m∠CFE + 2·m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementaryThe correct option is therefore;
inscribed angles; substitution property of equalityInscribed angles are angles formed by the intersection of two chords of
a circle.
The substitution property of equality states that variables that are
equal can be substituted by each other in any equation with both sides
of the the equation remaining equal.
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Jims fish bowl contains x tetras, 3 goldfish, and 5 platies. He removes one fish from the fish bowl at random. If the probability of removing a gold fish from the bowl is 1 out of 3 , how many tetras does jim have.
Answer: x = 1
Step-by-step explanation:
we have
x tetras
3 goldfish
5 platies.
the total number of fishh in the bowl is x + 3 + 5
The probability of removing a gold fish is equal to the number of gold fish divided by the total number of fish, this is:
p = 3/(x + 3 + 5) = 1/3
3 = (1/3)(x + 3 + 5) = x/3 + 1 + 5/3
9 = x + 3 + 5
x = 9 - 8 = 1
then wemust have that x = 1
because 1 + 3 + 5 = 9
and 3/9 = 1/3
What is a intersection
Answer:
Intersection means a line common to other lines and an action of intersection/intersecting.
hope it helps!
Use a geometric model to factor 2x2 - x - 1 by following
these steps:
Step 1: Model the polynomial by placing tiles in the
Product section.
Answer: It is not a perfect rectangle
Step-by-step explanation: Put 2 x2 tiles side by side horizontally then place an -x tile be side it then an - tile next to the x tile
Answer:
Step 4: What is the factored form of this trinomial?
✘ O A. (2[tex]x[/tex] - 1 ) ( [tex]x[/tex] + 1 )
✔ ∅ B. (2[tex]x[/tex] + 1 ) ( [tex]x[/tex] - 1 )
✘ O C. (2[tex]x[/tex] - 1 ) ( [tex]x[/tex] - 1 )
Anwar selects a playing card at random from the following 666 cards:
\{{left brace 999 of hearts, 555 of spades, 666 of hearts, 222 of spades, 444 of hearts, 777 of hearts\}}right brace
Let AAA be the event that Anwar selects an even-numbered card and BBB be the event that she chooses a heart.
Which of the following statements are true?
Answer:
We have 6 cards.
9 of hearts
5 of spades
6 of hearts
2 of spades
4 of hearts
7 of hearts.
A is the event where Anwar selects an even numbered card.
B is the event where she choses a heart.
we have 3 even cards (and two of them are hearts)
we have 4 hearts (2 of them are even)
The probability of event A is Pa = 3/6 = 1/2
the probability of event B is = Pb = 4/6 = 2/3
The probability of event A and Event B is the number of heart cards with even numbers, that are 2 divided the total number of cards:
Paandb = 2/6 = 1/3
the probabilty of A if we know that B is true:
P(AIB) = 2/4 = 1/2 (this is because we have 4 hearts, and we know that 2 of those 4 cards are even)
the probability of B if we know that A is true:
P(BIA) = 2/3 (this is because we have 3 even cards, and 2 of them are hearts)
Answer:
A,B,C,E
Step-by-step explanation:
Khan.
TRUST ME!!!!!!!!!!!! THIS IS RIGHT!!!!!!!
At Your Town Bike Shop, handle bar streamers are sold in packs of two and beads for spokes are sold in sets of 10. Georgina purchases 2 packs of handle bar streamers and 3 sets of beads for $27.85 before tax. Alexis purchases 1 pack of streamers and 4 sets of beads for $26.30 before tax. If Nana wants to buy 3 packs of streamers and 6 sets of beads, how much will her bill be before tax?
Answer: her bill be before tax is $49.2
Step-by-step explanation:
Let x represent the cost of 1 pack of handle bar streamers.
Let y represent the cost of 1 set of beads for spokes.
Georgina purchases 2 packs of handle bar streamers and 3 sets of beads for $27.85 before tax. It means that
2x + 3y = 27.85- - - - - - - - - 1
Alexis purchases 1 pack of streamers and 4 sets of beads for $26.30 before tax. It means that
x + 4y = 26.3
x = 26.3 - 4y - - - - - - - - - 2
Substituting equation 2 into equation 1, it becomes
2(26.3 - 4y) + 3y = 27.85
52.6 - 8y + 3y = 27.85
- 8y + 3y = 27.85 - 52.6
- 5y = - 24.75
y = - 24.75/-5
y = 4.95
x = 26.3 - 4y = 26.3 - 4(4.95)
x = 26.3 - 19.8
x = 6.5
If Nana wants to buy 3 packs of streamers and 6 sets of beads, her bill before tax would be
(3 × 6.5) + (6 × 4.95) = 19.5 + 29.7
= $49.2
The scores for the Algebra 2 CFE are normally distributed with a mean score of 43 and
a standard deviation of 3.8. If you scored 47 on the test, what percentage of test takers
scored lower than you? Do not round your answer. [percent]
Answer:
85.375%
Step-by-step explanation:
We would be using the z-score formula which is
z = (x-μ)/σ, where
x is the raw score,
μ is the population mean, and
σ is the population standard deviation.
In the question, we are given:
x is the raw score = 47
μ is the population mean = Mean score = 43
σ is the population standard deviation = 3.8
z = (x-μ)/σ
z = (47- 43)/ 3.8
z = 4/3.8
z = 1.0526315789
The z score = 1.0526315789
Checking my z score on my normal distribution table,
The percentage of test takers that scored lower than you =
[1 - P(x>Z)] × 100
= ( 1 - 0.14625) × 100
= 0.85375 × 100
= 85.375%
Therefore, the percentage of test takers that scored lower than you is 85.375%
A scale drawing is shown for clubhouse. The measurements are 4“ x 8“ what will the actual clubhouse measurements be if the scale factor is 1 inch equals 2 feet
Answer:
8ft. x 16ft.
Step-by-step explanation:
If each inch is scaled to 2 ft, then you simply multiply the values by two. The new scaled dimensions would be 8 x 16 ft. Hope this helps.
One of the solutions of the system of equations shown in the graph has an x-value of -4. What is its corresponding integer y-value?
-1
-3
0
3
Answer:
The 1st intersection P(x, y) has x = -4 and y = -3 (as shown in graph).
Option B = -3 is correct.
Hope this helps!
:)
The y intercept value is option (B) -3
What is x intercept and y intercept?The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis
Given
x intercept value = -4
From the graph we can say that y intercept value = -3
The y-intercept is the point where the line crosses the y-axis that is -3
Hence, the y intercept value is option (B) -3
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Anne wants to create a data display to summarize prices of the 264 homes for sale in her
area. A sample of the data is shown below.
$72,000, $129,500, $132,000, $149,400, $152,000, $183,500, $225,000, $289,000, $348,000
She wants the display to show how many homes are available for homebuyers with various
budgets. Which data display is best for Anne's purpose?
a histogram, because the minimum and maximum values are clearly displayed
a box plot, because the median is clearly displayed
a box plot, because the data are divided into four ranges of values
a histogram, because the bars show the frequency of data points within different ranges
Answer:
The correct option is (D).
Step-by-step explanation:
The boxplot is a consistent way to exhibit the data-distribution based on, minimum, first quartile, median, third quartile and maximum.
Therefore we can say it provides information about the location of the center, dispersion and skewness (measure of asymmetry) of the data.
The methods commonly used for depicting a frequency distribution are:
Histogram/Column graph Bar graph Frequency Polygon Pie chartOut of these, one of the most general and extensively used devices of illustrating a frequency distribution is the histogram.
In this case it is provided that Anne wants the display of prizes to show how many homes are available for home buyers with various budgets.
So, Anne can set range of budget values and assign the number of buyers with various budgets.
From the provided data the range of budget values can be set as:
Less than $50,000
$50,000 - $100,000
$100,000 - $150,000
$150,000 - $200,000
$200,000 - $250,000
$250,000 - $300,000
$300,000 - $350,000
Thus, the histogram data display is best for Anne's purpose.
The correct option is (D).
This question is based on the concept of statistics. Therefore, the histogram data display is best for Anne's purpose. Hence, the correct option is D, histogram.
Given:
Anne wants to create a data display to summarize prices of the 264 homes for sale in her area. A sample of the data is shown below.
$72,000, $129,500, $132,000, $149,400, $152,000, $183,500, $225,000, $289,000, $348,000.
According to the question,
As we know that, the boxplot is consistent way to exhibit the data distribution based on the minimum, first quartile, median, third quartile and maximum.
Therefore, it provides information about the location of the center, dispersion and skewness (measure of asymmetry) of the data.
The following methods commonly used for depicting a frequency distribution are:
Histogram/Column graph Bar graph Frequency Polygon Pie chartOut of these, one of the most extensively used devices of illustrating a frequency distribution is the histogram.
In this question it is provided that, Anne wants the display of prizes to show how many homes are available for home buyers with various budgets.
Thus, Anne can set range of budget values and assign the number of buyers with various budgets.
From the given data the range of budget values can be written as:
Less than $50,000
$50,000 - $100,000
$100,000 - $150,000
$150,000 - $200,000
$200,000 - $250,000
$250,000 - $300,000
$300,000 - $350,000
Therefore, the data display is best for Anne's purpose. Hence the correct option is D, histogram.
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select two values of x that are roots of this equation (picture included)
x^2+2x-5=0
Answer:
B and D
Step-by-step explanation:
i took this test
The roots of the equation will be - 1 - √6 and - 1 + √6. Then the correct options are B and D.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The quadratic equation is given below.
x² + 2x - 5 = 0
The solution of the quadratic equation will be
x² + 2x - 5 = 0
Add 1 on both sides, then the equation will be
x² + 2x + 1 - 5 = 1
x² + 2x + 1 = 1 + 5
(x + 1)² = 6
Taking square root on both sides, then the equation will be
x + 1 = ±√6
x = - 1 ±√6
Then the roots of the equation will be - 1 - √6 and - 1 + √6.
Then the correct options are B and D.
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What are our “cheat words” for finding slope?
Answer: y-intercept
Step-by-step explanation:
Zero is___ a divisor always sometimes never
Answer:
sometimes
Step-by-step explanation:
You can never divide a non-zero number, such as 3 or 7, by zero. However, you can divide zero by zero, so the answer is sometimes.
Hope this helped! :)
Answer:
sometimes
Step-by-step explanation:
Consider the trinomial x2 - 9x + 18.
Which pair of numbers has a product of ac and a sum
of b?
Answer:
the answer is -6 and -3
Step-by-step explanation:
Answer:
-3 and -6.
Step-by-step explanation:
ac = 1 *18 = 18
b = -9
The 2 numbers required are -3 and -6.
solve |-4|/|-4| please help
Answer:
i think the answer is 1 dont take my word for it though
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
The absolute value of -4 is 4, therefore |-4|/|-4| = 4/4 = 1
Which of the following are whole numbers ?
Answer:
-1 and 3 should be right
Answer:
3
Step-by-step explanation:
Whole numbers are non-negative integers
A whole number can be 0 or positive with decimal/fraction part
factor the binomials using gcf 16p + 4
What does Keaton spend the most money on?
Keaton's Monthly Spending
What does Keaton spend the least money on?
Food
Keaton spends about as much money on rent as he
does on
Rent
Clothes
Hygiene Products
Entertainment
Answer:FOOD, HYGIENE, ENTERTAINMENT
Step-by-step explanation:
The answer is:
foodHygiene ProductsEntertainmentWhat is Data?Data is referred to as a collection of information gathered by observations, measurements, research, or analysis. It may comprise facts, figures, numbers, names, or even general descriptions of things. Data can be organized in the form of graphs, charts, or tables for ease in our study. Data scientists help in analyzing the collected data through data mining.
According to the given information
a)Keaton spend the most money on Food.
b) Keaton spend the least money on Hygiene Products.
c) Keaton spends about as much money on rent as he does on Entertainment.
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slove the x in the digram below explain
Answer:
x= 20
Step-by-step explanation:
a flat angle is, in terms of geometry, the space between an intersection between two lines whose opening measures 180 degrees or 180º. Since the angle is 180º there is no difference between two lines or a line and we can say that the angles in a straight line always add up to 180º.
Step 1
define
according to the graph
3x+80+2x=flat angle=180°
3x+80+2x=180°
Step 2
solve for x
3x+80+2x=180°
5x+80=180
subtract 80 in each side
5x+80-80=180-80
5x=100
divide by 5
(5x)/5=100/5
x=20
happy to help:)
Find the midpoint of the segment with the following endpoints. (6,8) and (10,4)
Answer:
(8.6)
Step-by-step explanation:
To find the x coordinate of the midpoint, find the average of the x coordinates
(x1+x2)/2 = (6+10)/2 = 16/2 = 8
To find the y coordinate of the midpoint, find the average of the y coordinates
(y1+y2)/2 = (8+4)/2 = 12/2 = 6
Answer:
(8,6)
Well my explanation might be weird...so I won't explain it but I'm pretty sure I got the correct answer:>
The ratio of the leg opposite to an angle to the hypotenuse of a right triangle is
called the ____ of the angle.
A. sine
B. secant
C. cosine
D. cosecant
Answer:
cosine I think
Step-by-step explanation:
The ratio of the perpendicular and the hypotenuse is given by the sine of the angle. Then the correct option is A.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
The ratio of the leg opposite to an angle to the hypotenuse of a right triangle is called the sine of the angle.
The sine is given as the side opposite to the angle is known as perpendicular.
The ratio of the perpendicular and the hypotenuse is given by the sine of the angle.
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For his hiking club, Ricardo is making a container of trail mix with 3.5 kilograms of nuts. He has 1.78 kilograms of almonds. The rest of the nuts will be cashews. How many kilograms of cashews does he need? Use estimation to check your answer for reasonableness.
Answer: 1.72 kilograms
Step-by-step explanation:
From the question, Ricardo is making a container of trail mix with 3.5 kilograms of nuts and he has 1.78 kilograms of almonds while the remaining of the nuts will be cashews.
To get the kilograms of cashews nuts that are needed, we subtract the kilograms of almonds from the total container. This will be:
= 3.5 kg - 1.78 kg
= 1. 72 kg
Find the area of this circle. Use 3.14 for piπ.
Answer:
A =452.16 ft^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = 3.14 (12)^2
A =452.16 ft^2
Answer:
452.16ft^2
Step-by-step explanation:
So to answer this You need to use the formula A=πR^2
Step one is Figuring out what the equation is so A= (3.14)12^2Now what is 12 squared? The answer is 144ftStep three Multiply 144 by 3.14 since that is for PI to get 452.16ft^2Using laws of Sines. Find the measurement indicated. Round your answers to the nearest tenth.
Answer:
see below
Step-by-step explanation:
8.
We have to use the law of cosines to find AB
c^2 = a^2 + b^2 − 2ab cos(C)
AB^2 = 14^2 + 24^2 - 2 * 14 *24 cos(91)
AB^2 =196 +576 - 672 cos(91)
AB^2 =783.7280171
Taking the square root of each side
AB =27.99514
Rounding to the nearest tenth
AB = 28
(If the lengths are supposed to have the variable A)
AB = 28A
9.
Using the law of sines
sin 84 sin A
-------------- = -------------
22 9
Using cross products
9 sin 84 = 22 sin A
Divide each side by 22
9 sin 84 /22 = sin A
.406849866 = sin A
Taking the inverse sin of each side
24.00710132 = A
To the nearest tenth
A = 24
Answer:
AB = 28 ft; m<A = 24 deg
Step-by-step explanation:
8.
Since you are not given an angle and its opposite side, you cannot start with the law of sines. You must use the law of cosines.
[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]
[tex] c^2 = (14~ft)^2 + (24~ft)^2 - 2(14~ft)(24~ft) \cos 91^\circ [/tex]
[tex] c^2 = 196~ft^2 + 576~ft^2 - 672~ft^2(-0.01745) [/tex]
[tex] c = \sqrt{783.73~ft^2} [/tex]
[tex] c = 27.995~ft [/tex]
AB = c = 28 ft
9.
[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} [/tex]
[tex] \dfrac{\sin A}{9~km} = \dfrac{\sin 84^\circ}{22~km} [/tex]
[tex] \sin A = \dfrac{9~km~\sin 84^\circ}{22~km} [/tex]
[tex] \sin A = 0.40685 [/tex]
[tex] A = \sin^{-1} 0.40685 [/tex]
[tex] A = 24^\circ [/tex]
A scientist created a scatterplot to display the height of a plant over a 12-day period. Plant Height A graph has days on the x-axis and height (inches) on the y-axis. A trend line goes through points (5, 3) and (12, 7). Which is the equation of the trend line that is shown? y = StartFraction 1 Over 7 EndFraction x + StartFraction 4 Over 7 EndFraction y = StartFraction 1 Over 7 EndFraction x + StartFraction 16 Over 7 EndFraction y = StartFraction 4 Over 7 EndFraction x minus StartFraction 1 Over 7 EndFraction y = StartFraction 4 Over 7 EndFraction x + StartFraction 1 Over 7 EndFraction
Answer:
The correct option is (D) [tex]y=\frac{4}{7}\ x+\frac{1}{7}[/tex].
Step-by-step explanation:
The two-point form for the equation of straight line is:
[tex](y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})[/tex]
The two points provided are:
A = (5, 3)
B = (12, 7)
Compute the equation of the trend line as follows:
[tex](y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})\\\\(y-3)=\frac{7-3}{12-5}\ (x-5)\\\\(y-3)=\frac{4}{7}\ (x-5)\\\\y-3=\frac{4}{7}\ x-\frac{20}{7} \\\\y=\frac{4}{7}\ x-\frac{20}{7}+3\\\\y=\frac{4}{7}\ x+\frac{-20+21}{7}\\\\y=\frac{4}{7}\ x+\frac{1}{7}[/tex]
Thus, the equation of the trend line is [tex]y=\frac{4}{7}\ x+\frac{1}{7}[/tex].
The correct option is (D).
Answer:
D
Step-by-step explanation:
plz help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Donna took twice as long to drive 720 miles and Maple took to drive 200 miles. Find the rates and ties of both if Donna's speed exceeded that of Maple by 40 miles per hour
Answer:
Donna traveled for 8 hours at 90 mph
Maple traveled for 4 hours at 50 mph
Step-by-step explanation:
The velocity at which each person traveled is given by the distance traveled divided by the time spent (t). From the information given, the following expressions can be written
[tex]t_d = 2t_m\\V_d = V_m+40\\V_d = \frac{720}{t_d}\\V_m = \frac{200}{t_m}\\\\V_d = \frac{360}{t_m}\\ \frac{360}{t_m}=\frac{200}{t_m}+40\\t_m = 4\ hours\\t_d=2*4 = 8\ hours\\\\V_d = \frac{720}{8}=90\ mph\\V_m = \frac{200}{4}=50\ mph\\[/tex]
Therefore, Donna traveled for 8 hours at 90 mph and Maple traveled for 4 hours at 50 mph.
Determine the vertex of the function f(x) = 3x2 – 6x + 13.
1. Identify the values of a and b.
a =
and b =
2. Find the x-coordinate of the vertex.
negative StartFraction b Over 2 a EndFraction =
3. Find the y-coordinate by evaluating the function at the x-value found in the previous step.
The vertex is
.
Answer:
1.)
A=3
B=-6
2.)
1
3.)
(1,10)
Answer:
1. Identify the values of a and b.
a =
✔ 3
and b =
✔ –6
2. Find the x-coordinate of the vertex.
negative StartFraction b Over 2 a EndFraction =
✔ 1
3. Find the y-coordinate by evaluating the function at the x-value found in the previous step.
The vertex is
✔ (1, 10)
1. The cost to rent a movie is $3 for 1 day,
$4 for 2 days, and $5 for 3 days. Describe
the relationship between the cost and the
number of days.
2. Kenji plants 8 seeds in 1 row of his garden,
16 seeds in 2 rows, and 24 seeds in 3 rows.
Describe the relationship between the
number of rows and the number of seeds.
Answer:
i dont really know
Step-by-step explanation:
The price goes up by 1 for every 1 day. 2 times the amount as seeds per day.
8 x 2 = 16 8 x 3 = 24.
