A right triangle is formed by the x-axis, the y-axis, and the line y = -2x + 7.A. Sketch and label a graph of the triangle in the coordinate plane.B. Find the length of the hypotenuse.C. Find the area of the triangle.
Answers
The given equation is
[tex]y=-2x+7[/tex]We have to find the axis interceptions to graph this function.
For x = 0, we have
[tex]y=-2(0)+7=0+7=7[/tex]The y-interception is (0,7).
For y = 0, we have
[tex]\begin{gathered} 0=-2x+7 \\ 2x=7 \\ x=\frac{7}{2} \end{gathered}[/tex]The x-interception is (7/2, 0).
Now, we graph.
Where h is the hypothenuse.
To find the hypothenuse of the right triangle formed, we use the distance formula and both points.
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]Replacing the coordinates, we have
[tex]\begin{gathered} d=\sqrt[]{(0-7)^2+(3.5-0)^2}=\sqrt[]{(-7)^2+(3.5)^2} \\ d=\sqrt[]{49+12.25}=\sqrt[]{61.25}\approx7.83 \end{gathered}[/tex]Therefore, the hypotenuse is 7.83 units long, approximately.
At last, the area of the triangle is found with the formula
[tex]A=\frac{1}{2}b\cdot h[/tex]Where b is the base and h is the height of the triangle. b = 3.5, h = 7.
Replacing these values, we have
[tex]A=\frac{1}{2}(3.5)\cdot(7)=\frac{24.5}{2}=12.25u^2[/tex]Therefore, the area of the triangle is 12.25 square units.
Related Questions
Find the radius of the piñata in feet. near to nearest hundredth.
Answers
Explanation:
The formula is given below as
[tex]\begin{gathered} S=4\pi r^2 \\ where, \\ S=surfacearea=60ft^2 \\ r=radius \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} S=4\pi r^{2} \\ 60=4\pi r^2 \\ r^2=\frac{60}{4\pi} \\ r^2=\frac{15}{\pi} \\ square\text{ root both sides } \\ r=\sqrt{\frac{15}{\pi}} \\ r=2.19 \end{gathered}[/tex]Hence,
The final answer to the nearest hundredth is
[tex]2.19[/tex]Write the equation of a line that passes through the points (-1, 3)and (2,6)
Answers
The equation of a line in 2 point form is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]So, inputting the points, we have
[tex]\begin{gathered} \frac{y-3}{x+1}=\frac{6-3}{2+1} \\ \frac{y-3}{x+1}=\frac{3}{3}=1 \\ \text{cross multiply} \\ y-3=x+1 \\ y=x+4 \end{gathered}[/tex]So, the equation of our line is y = x + 4
Statistics questions pictured in attachment.
Answers
Using the normal distribution, it is found that:
a) The variable used in this problem is: The time (in hours) a 4-year old spends unsupervised per day.
b) The distribution is: X ~ N(3, 1.8).
c) The probability is P(X < 1) = 0.1335, and is given by the bottom left graph.
d) The percentage of children who spend over 10 hours a day unsupervised is of 0.01%.
e) 90% of the children spend at least 0.7 hours unsupervised.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.The variable used in this problem is:
The time (in hours) a 4-year old spends unsupervised per day, as the distribution involves only 4-year old children, and the mean and the standard deviation are measured in hours.
The mean and the standard deviation of the distribution are given, respectively, by:
[tex]\mu = 3, \sigma = 1.8[/tex].
Hence the distribution can be described approximately as follows:
X ~ N(3, 1.8).
The probability that a person spends less than 1 hour a day unsupervised is the p-value of Z when X = 1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1 - 3)/1.8
Z = -1.11
Z = -1.11 has a p-value of 0.1335.
The bottom left graph shows this probability, as the number in hours cannot be less than 0(there is no negative number of hours).
The proportion of children who spends over 10 hours a day unsupervised is one subtracted by the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (10 - 3)/1.8
Z = 3.89
Z = 3.89 has a p-value of 0.9999
1 - 0.9999 = 0.0001, hence the percentage is of 0.01%.
For item e, the measure is the 10th percentile, which is X when Z = -1.28, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-1.28 = (X - 3)/1.8
X - 3 = -1.28 x 1.8
X = 0.7 hours.
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. how many 1/4s are in 6
Answers
Let us divide 6 by 1/4
6/1 ÷ (1/4)
6/1*4/1 (Turning the second fraction upside down and multiplying it by the first fraction)
24 (Multiplying)
The answer is 24.
Answer:
Step-by-step explanation:
Since there are four 1/4 in 1 then you have to multiple 6*4= 24!
Find the equation of a line with given slope and containing given point. Write the equation in sole-intercept m= -7/2, point (-8,-4)
Answers
Given:
There are given that the slope and the point:
[tex]\begin{gathered} m=-\frac{7}{2} \\ point:\left(-8,-4\right) \end{gathered}[/tex]Explanation:
To find the equation, first, we need to see the formula for slope-intercept form:
So,
From the slope-intercept formula;
[tex]y=mx+b[/tex]Where,
[tex]\begin{gathered} m=-\frac{7}{2} \\ \lparen x,y)=\left(-8,-4\right) \end{gathered}[/tex]Now,
We need to find the value of b by using given information:
So,
Put all the given values into the given slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ -4=-\frac{7}{2}\left(-8\right)+b \\ -4=28+b \\ b=-32 \end{gathered}[/tex]Then,
Put the value of b and m into the slope-intercept form;
So,
[tex]\begin{gathered} y=mx+b \\ y=-\frac{7}{2}x+\left(-32\right) \\ y=-\frac{7}{2}x-32 \end{gathered}[/tex]Final answer:
Hence, the equation of a line is shown below;
[tex]y=-\frac{7}{2}x-32[/tex]Albert is in a hot air balloon that has just taken off and is now floating 20 meters above its
launching point Isabelle is standing on the ground, 21 meters away from the launching point.
How far apart are Albert and Isabelle?
meters
Answers
Albert floating in hot air balloon and Isabelle standing at ground are 29 meters far apart from each other.
What is hot air balloon?
A hot air balloon is a lighter in weigh than air. It is an object made up of an envelope-like bag that holds heated air. A wicker basket, gondola, or capsule suspended below transports people and a heat source, typically an open flame produced by burning liquid propane. A capsule also carries passengers in some long-distance or high-altitude balloons.
Lets understand with the help of a right angle triangle, The point from where the hot air balloon taken off be point A, and the point where Isabelle is standing is point B, and the point where the balloon is point C.
The AB= distance between Isabelle and the point from where hot air balloon taken off = base of the imagined triangle,
AC = height at which hot air balloon is floating = perpendicular of the imagined triangle
BC = distance between Isabelle and hot air balloon = Hypotenuse of the imagined triangle
Applying Pythagoras theorem,
(BC)² = (AC)² + (AB)²
(BC)² = (20)² + (21)²
BC = 29
Hence Albert and Isabelle are 29 meters far apart.
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Given f(x) = 4x -5; what is f(4)?
Answers
so if f(x)= 4x-5, f(4)= 4•4 -5= 16-5
=11
The graph of f is given below. Use the graph to determine the following items.
• The z-values, if any, where f has a relative maximum.
• The value(s), if any, of the relative maximum(s) of f.
• The z-values, if any, where f has a relative minimum.
• The value(s), if any, of the relative minimum(s) of f.
Answers
Part 1
Relative maxima are where the function changes from increasing to decreasing.
No x-values satisfy this.Part 2
None, see above.
Part 3
Relative minima are where the function changes from decreasing to increasing.
No x-values satisfy this.Part 4
None, see above.
0.25(8+x)=14 I understand just not fully
Answers
25(8+ x)=14
25*8+ 25x =14
200+ 25x= 14
25x=14-200
25x = -186
x = -186/25
x= -7.44
evaluate the expression 2x + 3 when x = 1.6
Answers
Given the following expression:
[tex]2x+3[/tex]You need to follow the steps shown below in order to solve the exercise:
1. Since you know the value of "x", you must substitute it into the given equation:
[tex]2x+3=2(1.6)+3[/tex]2. Now you must solve the multiplication:
[tex]=3.2+3[/tex]3. Finally, you need to solve the addition in order to find the value of the expression. Therefore, you get that the result is the following:
[tex]=6.2[/tex]The answer is:
[tex]=6.2[/tex]Find the length of the diameter of the circle
with the following equation: (x-4)^2+(y-2)^2=5
Answers
The length of the diameter of the circle is found as the 2×(√5).
What is termed as the equation of the circle?The equation of circle offers an algebraic method for describing a circle given its center and radius length. The equation of a circle differs from the formulas used to calculate a circle's area or circumference. The standard equation for a circle with a radius r and a center at (x1,y1) is: (x−x1)²+(y−y1)²=r².,
For the given question;
The equation of the circle is given as;
(x-4)^2+(y-2)^2=5
Comparing the equation of the circle with the standard form.
Radius r² = 5
Then, r = √5
Now, the diameter is the twice of the radius.
Diameter = 2×radius
Diameter = 2×(√5)
Thus, the length of the diameter of the circle is found as the 2×(√5).
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Working together, Adam and Pranav can mop a warehouse in 4.63 hours. Had he done it alone it would have taken Pranav 11 hours. How long would it take Adam to do it alone?
Answers
1)
Note that the more people work together the less time they spend.
This is a question about Proportions, Inverse variation. So let's set the ratios and the proportion given these data.
So we can write out the following ratios:
[tex]\begin{gathered} \frac{1}{x}+\frac{1}{11}=\frac{1}{4.63} \\ \\ \frac{x+11}{11x}=\frac{1}{4.63} \\ \\ 4.63(x+11)=11x \\ 11x=4.63(x+11) \\ 11x-4.63x=11 \\ 6.37x=11 \\ \frac{6.37x}{6.37}=\frac{11}{6.37} \\ x=7.99\approx8 \end{gathered}[/tex]So, it would take 8 hours for Adam to do it alone.
Which of the following side lengths would create a right triangle? Select all
that apply.
5, 5, 10
3,4,7
12, 16, 20
4.5, 6, 7.5
11, 60, 61
6,9, 10
3, 4, 12
8, 15, 17
Answers
Answer:
5,12,13
Step-by-step explanation:
first you write out a^2 or a squares + b^2=C ^2 You plug in for a and b the smaller numbers then for c you put the biggest number. Now square everything. And you should get 25 for a. 144 for b. 169 for c. Now add a and b which is25+144 and that equals 169. So 5,12,13 is your answer.
Match the pairs of angles formed by the parallel lines and transversal to their correct vocabulary identification
Answers
The angles that are formed by the parallel lines and the transversal are:
1. Vertical Angles
2. Same-side Exterior Angles
3. Corresponding Angles
4. Alternate Interior Angles
5. Alternate Exterior Angles
6. Same-side Interior Angles
7. Adjacent Angles
What are Special Angle Pairs that are Formed by Parallel Lines and Transversal?The following are special angle pairs that are formed when a transversal intercepts two parallel lines:
1. Vertical Angles: These are nonadjacent angles that share the same vertex and are directly opposite each other. An example of such angle pair is angle 6 and angle 7.
2. Same-side Exterior Angles: These are exterior angles that lie on the same side of a transversal but on sperate parallel lines. Example include angle 2 and angle 8.
3. Corresponding Angles: These angles are located on each parallels lines that are cut across by a transversal and lie relatively in the same corner to each other. An example is, angle 1 and angle 5.
4. Alternate Interior Angles: an example of such pair of interior angles that lie on opposite side of a transversal is, angle 3 and angle 6.
5. Alternate Exterior Angles: An example of a pair of alternate exterior angle is angle 2 and 7.
6. Same-side Interior Angles: These pair of angles are interior angles on the same side of a transversal. Example of such pair of angles is, angle 4 and angle 6.
7. Adjacent Angles: These are angles that share a common side and a vertex, an example is: angle 1 and angle 2.
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QUESTION 3 Round the following to the most appropriate whole number. The ratio of children to adults at an amusement park is typically 5 to 3. 201 adults are in the park. How many children should be in the park?
Answers
335 children should be in the park, if the ratio of children to adults at an amusement park is typically 5 to 3 and 201 adults are in the park.
What is ratio?A ratio is the comparison of two similar quantities or the proportion of one similar quantity to another. With the same meaning, ratios can be expressed in three different ways using words or symbols. In other words, ratios can be expressed by sandwiching a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.
The ratio of ninth-graders to tenth-graders can take on any of the three forms listed below, using the previous example of comparing the two groups of students in Ms. Jones' class:
10 /20
10 to 20
10 : 20
Given ratio of children to adults is 5:3
5 + 3 = 8
5/8 are children and 3/8 are adults
Let the total no. of people be x
3/8 = 201/x
x = 201 × 8/3
= 536
Now. no. of children is
5/8 × 536
= 335
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Here’s the question. Let me know when u have the answer. Also, this is just apart of a homework practice
Answers
Let f(x) be a function; thus, the reflection across the y-axis of f(x) is given by f(-x).
Therefore, in our case,
[tex]g(x)=f(-x)=-(-x)^3-8(-x)^2-9(-x)+11[/tex]Simplifying,
[tex]\Rightarrow g(x)=x^3-8x^2+9x+11[/tex]Thus, the answer is g(x)=x^3-8x^2+9x+11, the first option (top to bottom).
which of the following polynomials is in standard form?y^12-y^15+y^10-4yz^5+z^3-z^2-42z^3+z^5-9x+x^2+x^3+x^4
Answers
For a polynomial to be in standard form, the terms are arranged from the highest exponent to the lowest exponent.
Thus, from the polynomials given, the polynomial in standard form is:
[tex]z^5+z^3-z^2-4[/tex]This is because the term with the highest exponent is the first term, the next exponent is 3, followed by the term with an exponent of 2, then the last term is the term with the least exponent.
ANSWER:
[tex]z^5+z^3-z^2-4[/tex]help me please
thank you
Answers
Answer:
Domain: A, [tex)(-\infty, \infty)[/tex]
Range: [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
çok acill çözüm lütfeen
Answers
Answer: it is yes
Step-by-step explanation:
When the crate folow top botom nuberto
The domain for the relation below is {x| -6
Answers
We need to find the point given the domain and range of the relation:
For domain and range, the result includes the number. Hence, the end values are given by the points.
For point C:
(-6,4)
Because point c is on quadrant two, where x is negative and y is positive.
Also, it takes the higher y value.
For point D:
(6,3)
Because point D is on quadrant 1, where x is positive and y is also positive.
.
The floor of an elevator shaft is a square with an area of 42.25 square feet. Find the length of
a side of the floor.
Chapter 2 Expor
Answers
Answer:
6.5ft
Step-by-step explanation:
[tex]A=s^{2} \\42.25=s^{2} \\\sqrt[2]{42.25}=\sqrt[2]{s} \\6.5=s[/tex]
Answer:
6.5ft
Step-by-step explanation:
Order the expressions by choosing <, >, or =.
Answers
On comparing the given expressions we get-
[tex]9^{-2} < (\frac{1}{9}) ^{-1}[/tex]
[tex](\frac{1}{9}) ^{-1} < (\frac{1}{9}) ^{-2}[/tex]
[tex]9^{-1} > 9^{-2}[/tex]
Here, we are given 3 pairs of expression. Let us evaluate them one by one.
[tex]9^{-2}[/tex] _ [tex](\frac{1}{9}) ^{-1}[/tex]
The negative exponent means that the base is the reciprocal raised to a positive power. Thus, [tex]9^{-2}[/tex] can be written as- [tex](\frac{1}{9}) ^{2}[/tex] = 1/81
similarly, [tex](\frac{1}{9}) ^{-1}[/tex] can be written as- [tex](9}) ^{1}[/tex] = 9
Thus, the expression becomes-
1/81 _ 9
clearly we can see that 1/81 < 9
Now, we have [tex](\frac{1}{9}) ^{-1}[/tex] _ [tex](\frac{1}{9}) ^{-2}[/tex]
As shown above, the expression can be simplified as-
[tex](9) ^{1}[/tex] _ [tex](9) ^{2}[/tex]
9 _ 81
clearly we can see that 9 < 81
Next, we have- [tex]9^{-1}[/tex] _ [tex]9^{-2}[/tex]
we can write this as-
1/9 _ 1/81
Clearly, 1/9 > 1/81
Hence, we have solved the given inequalities.
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The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 91 square centimeters?
____ cm/min
Answers
dA = (1/2)h(db) + (1/2)b(dh).
4 = (1/2)(8.5)db + (1/2)(194/8.5)(2.5), db = (4 - (1/2)(194/8.5)(2.5))/((1/2)(8.5)) =-5.77 cm/min.
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Related questions (More answers below)
From a hot-air balloon, Guadalupe measures a 31 degree angle of depression to a landmark thats 316 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary
Answers
We will first sketch the problem
Let x be the vertical distance above the ground
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]\tan 31=\frac{x}{316}[/tex]cross-multiply
[tex]x=316\tan 31^o[/tex][tex]x\approx189.9[/tex]481,462 rounded to the nearest hundred thousand
Answers
Answer: 500,000
Step-by-step explanation: To round the numbers their nearest hundred thousand, first we have to make the first five digits into the lower number that ends with zero
Example: 52437 is rounded to the nearest hundred thousand is 52000
Sorry if you don't understand I'm just bad at explaining :) T^T
Write an equation in slope - intercept form for the line that passes through the given paint andis parallel to the given equation.(9, 12), y = 13x-4
Answers
The equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope of the line and (x1,y1) is a point where the line passes through.
In our case we have a point but we don't have the slope yet, so we have to find it. To do this we have to remember that two lines are parallel if and only if their slopes are equal, that is
[tex]m_1=m_2[/tex]We know that the line we are looking for is parallel to the line
[tex]y=13x-4[/tex]we notice that this line in written in the slope-intercept form
[tex]y=mx+b[/tex]then its slope is 13.
Since the line is parallel to the one we are looking for, our slope is also 13.
Using the point (9,12) and the slope the equation of the line is
[tex]y-12=13(x-9)[/tex]now we have to write in the slope-intercept form
[tex]\begin{gathered} y-12=13x-117 \\ y=13x-117+12 \\ y=13x-115 \end{gathered}[/tex]Therefore the line is
[tex]y=13x-115[/tex]SET A
15 points
Hi to everyone I just need an answer for my activity one of my subject
thank you:)
Answers
Answer:
8 points for solving 6 questions?? Nah thats worth 25 points
Step-by-step explanation:
One 60-to-65 year old man is selected at random. What is the probability of the following events?
Answers
The probabilities that have been calculated here are:
0.240.890.3330.0395How to solve for the probabilitiesThe probability that he is a smoker = 0.08 + 0.16
= 0.24
The given probability that has been calculated is 0.24.
The probability that he does not have lung disease = 0.16 + 0.73
= 0.89
The probability that he has lung disease given that he is a smoker
= 0.08 / 0.08 + 0.16
= 0.08 / 0.24
= 0.333
The probability here is calculated to be 0.333
The probability that he has lung cancer given that he does not smoke
= 0.03 / 0.03 + 0.73
= 0.03 / 0.76
= 0.0395
The given probability here is 0.0395
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Use slope to determine if lines AB and CD are parallel, perpendicular, or neither. 2. A(0,2), B(5, 4), C(1.8).D(3,3)m(TABm(CD)Types of Lines
Answers
A (0,2) B (5,4)
C(1,8) D( 3,3)
Apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]For AB
[tex]m=\frac{4-2}{5-0}=\frac{2}{5}[/tex]For CD
[tex]m=\frac{3-8}{3-1}=-\frac{5}{2}[/tex]So both slopes are negative reciprocals of each other.
They are perpendicular lines.
Factorise fully the following
9x^2+3x^3
Answers
Answer:
[tex]3x^2\left(3+x\right)[/tex]
Step-by-step explanation:
Look for common factor: [tex]3x^{2}[/tex] since we take the least exponent
and between numbers (3,9) the common factor is 3.
Thefore, we need to divide [tex]3x^2[/tex] by the equation.
[tex]3x^2(3+x)[/tex].
Step-by-step explanation:1. Write the expression.[tex]9x^2+3x^3[/tex]
2. Find a common denominator for both expressions, based on the x variable.[tex]\frac{9x^2}{3x^2} +\frac{3x^3}{3x^2} \\ \\3x^2(3+x)[/tex]
3. Express your result.[tex]9x^2+3x^3=3x^2(3+x)[/tex].
