For triangle ABC, ∡c=90°. Draw and label a diagram for this triangle, then find the measures of the remaining angles and sides. Explain how you found each measure.
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Given:-
[tex]\Delta ABC,\angle C=90[/tex]To find:-
Draw and label a diagram for this triangle, then find the measures of the remaining angles and sides. Explain how you found each measure.
At first construct an right angled triangle at c. so we get,
So now we need to use a protractor and measure the angle A and angle B.
Related Questions
Find the Discriminant and describe the number and type of solutions of the equations. 1) 4x^2 + 8x + 4 =0
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Given:
[tex]4x^2+8x+4=0[/tex]To find the discriminant, use the formula:
[tex]\Delta=b^2-4ac[/tex]Where a = 4, b = 8, c = 4
Thus, we have:
[tex]\begin{gathered} \Delta=8^2-4(4)(4) \\ \\ \Delta=64-64\text{ =0} \end{gathered}[/tex]The discriminant is = 0
To find the number of solutions, since the disriminant is zero, we have two real and identical roots.
ANSWER:
Discriminant = 0
Number of roots = 2 real and identical roots
Determine the smallest possible co-terminal
angle for a) 410. b)-45
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The smallest possible co-terminal are:
a)50
b) -495
Define co terminal angles.Angles that share the terminal side with an angle occupying the standard position are said to be co terminal angles. In the conventional position, the vertex is at the origin and one side of the angle is fixed along the positive x-axis.
In other words, two angles are co terminal when their vertices and sides are the same but their angles themselves differ.
Additionally, you can recall the concept of co terminal angles as angles that differ by an exact number of full circles.
Given Data
The smallest co terminal angle for:
a) 410
Divide the first number by the second, rounding down (towards the floor).
[tex]\frac{360}{410}[/tex]
= 1
after that, multiply the divisor by the result (called the quotient),
360(1)
= 360
Take this amount out of your starting amount.
410-360
= 50
b) -45
- 45 [tex]\frac{pie}{4}[/tex]
= -495
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After entering the table values in his calculator, Cory used the LinReg button to get the results shown. Identify the correlation coefficient and the type of correlation.
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The value of the correlation coefficient is -0.2985, and the relation between x and y is a weak negative option (B), and (D) are correct.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]
From the data given in the table,
The value of the correlation coefficient can be found using the formula:
r = -0.2984713607
After rounding off:
r = -0.2985
As the value of r is not near the -1 so the relation between x and y is weak negative:
Thus, the value of the correlation coefficient is -0.2985, and the relation between x and y is a weak negative option (B), and (D) are correct.
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Solve the triangle: a = 12,c = 2-2, B = 33". If it is not possible, say so.A= 25.1",b = 1.8, C = 121.9"This triangle is not solvable.A = 45*,b= V2.C = 102VEA= 30', b = -, C = 117"
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ANSWER:
A=25.1 degrees
b = 1.8
C = 121.9 degrees
SOLUTION:
We can solve this problem using the cosine law, since we are given the length of 2 sides of triangle and the angle they formed.
[tex]b\text{ =}\sqrt[]{c^2+a^2-2ac\cos B}[/tex]We substitute the given
[tex]\begin{gathered} b\text{ =}\sqrt[]{(2\sqrt[]{2})^2+(\sqrt[]{2})^2-2(\sqrt[]{2})(2\sqrt[]{2})\cos 33} \\ b\text{ = 1.8} \end{gathered}[/tex]Using Sine Law, we can get the angles
[tex]\begin{gathered} \frac{1.8}{\sin 33}=\frac{\sqrt[]{2}}{\sin A} \\ A=25.1 \end{gathered}[/tex]Since the total angle inside a triangle is 180, the angle at C is
[tex]C-33-25.1=121.9[/tex]This table shows the amount of gas Sharla's car uses to travel different distances on a highway.Number of Gallons Number of Miles41446216324912432Based on the data in the table, how many miles per gallon does Sharla's car get on a highway?O A. 18 mpgO B. 28 mpgOC. 36 mpgO D. 72 mpg
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We'll calculate the miles per gallon using the following formula and the data on the table:
[tex]\text{mpg}=\frac{miles\text{ traveled}}{\text{gallons used}}[/tex]From the first set of data:
[tex]\text{mpg}_1=\frac{144}{4}=36[/tex]From the second:
[tex]\text{mpg}_2=\text{ }\frac{216}{6}=36[/tex]From the third
[tex]\text{mpg}_3=\frac{324}{9}=36[/tex]and from the fourth
[tex]\text{mpg}_4=\frac{432}{12}=36[/tex]Since all the data on the table showed us that the car gets 36 miles per gallon, we can conclude that it indeed gets 36 miles per gallon.
Write a recursive formula for an, the nthterm of the sequence 8, -2, -12, ....
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We have the sequence: 8, -2, -12...
We can prove that this is an arithmetic sequence as there is a common difference d=-10 between consecutive terms.
Then, the recursive formula (the expression where the value of a term depends on the value of the previous term) can be written as:
[tex]a_n=a_{n-1}-10[/tex]Answer: the recursive formula is a1 = 8, a(n) = a(n-1) - 10
5. Four hamsters have a combined weight of 5.112 grams. If all the hamsters weigh the same, how many kilograms does one hamster weigh? kilograms
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We were told that Four hamsters have a combined weight of 5.112 grams. We know that
1000 grams = 1 kilogram
Thus,
5.112 grams = 5.112/1000
= 0.005112 kilograms
Since all the hamsters weigh the same, then the weight of one hamster is
0.005112 /4
= 0.001278 kilogram
The weight of one hamster is 0.001278 kilogram
Tyler wants to crate a scale drawing of his bedroom. His bedroom is a rectangle with length 5m and width 4m. He decides on a scale of 1 to 80
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The dimension of the rectangle after the scale will be 5 cm wide and 6.25 cm long.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
Tyler wants to sketch out his bedroom to scale. His bedroom is a rectangle that is 5 meters long and 4 meters wide. He chooses based on a scale of 1 to 80.
Then the dimension of the rectangle after the scale.
Width = (1/80) x 4
Width = 5 cm
Length = (1/80) x 5
Length = 6.25 cm
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use this figure for questions 1 through 4 1. are angles 1 and 2 a linear pair?2. are angles 4 and 5 a linear pair ?3.are angles 1 and 4 vertical angles?4. are angles 3 and 5 vertical angles ?
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Linear pair angles form a straight line, so, both angles add up to 180°.
1 and 2 are not a linear pair.
4 and 5 are a linear pair.
Vertical angles are opposite angles, that are equal.
1 and 4 are vertical angles
3 and 5 are NOT vertical angles-
Solve for x. (x-8a)/ 6 = 3a-2x
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Given the equation:
[tex]\frac{x-8a}{6}=3a-2x[/tex]To solve for x, first we move the 6 to the other side of the equation:
[tex]\begin{gathered} \frac{x-8a}{6}=3a-2x \\ \Rightarrow x-8a=(3a-2x)\cdot6 \end{gathered}[/tex]Since the 6 was dividing, we pass it to the other side multiplying. Now we apply the distributive property and move the term -8a to the other side:
[tex]\begin{gathered} x-8a=(3a-2x)\cdot6 \\ \Rightarrow x-8a=18a-12x \\ \Rightarrow x=18a-12x+8a \\ \end{gathered}[/tex]Finally, we move the -12 to the other side with its sign changed:
[tex]\begin{gathered} x+12x=18a+8a=26a \\ \Rightarrow13x=26a \\ \Rightarrow x=\frac{26}{13}a=2a \\ x=2a \end{gathered}[/tex]therefore, x=2a
help me please
thank you
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Answer:
Domain: A, [tex](-\infty, \infty)[/tex]
Range: A, [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.
Tow "N" Go Towing Company charges a flat fee of $75 plus an additional $5 for every mile the car is towed. Which function models the cost, T(), of towing a car for miles?
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Answer:
5N + 75 I believe
Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval.
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We have the following integral in the discrete sum form:
[tex]\lim_{||\Delta||\to0}\sum_{i\mathop{=}1}^{\infty}(6c_i+3)\Delta x_i.[/tex]In the interval [-9, 6].
To convert to the integral form, we convert each element of the discrete sum form:
[tex]\begin{gathered} \lim_{||\Delta||\to0}\sum_{i\mathop{=}1}^{\infty}\rightarrow\int_{-9}^6 \\ 6c_i+3\rightarrow6x+3 \\ \Delta x_i\rightarrow dx \end{gathered}[/tex]Replacing these in the formula above, we get the integral form:
[tex]\int_{-9}^6(6x+3)\cdot dx.[/tex]AnswerMay I please get help with this place. I have tried multiple times but still could not get the correct
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(a) Which figures are parallelograms.
A parallelogram is a quadrilateral whose opposite sides are parallel, and therefore opposite angles are equal.
Figure B, and C are parallelogram since all of the opposite angles are equal.
Figure A is also a parallelogram since the all of the opposite sides are congruent.
FIGURE A,B, and C are parallelograms.
(b) Which figures are rectangles.
A rectangle is a parallelogram where all of the angles are 90°. A square is also a type of rectangle where all the sides are congruent.
FIGURE B and C are rectangles.
(c) Which figures are squares.
As mentioned earlier, as square is a rectangle where all the interior angles is 90°, and has all of the sides congruent.
FIGURE C is a square.
I'll send a better pic I just need help doing the work and understanding what it's about
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The formula to calculate the rate of change is given to be:
[tex]r=\frac{y_2-y_1}{x_2-x_1}[/tex]In the question, time will be the x-variable while distance will be the y-variable.
QUESTION A: Between 0 and 1.
Between 0 and 1, we will use the following parameters to calculate the rate:
[tex]\begin{gathered} x_1=0 \\ x_2=1 \\ y_1=6 \\ y_2=4 \end{gathered}[/tex]Therefore, the rate is:
[tex]\begin{gathered} r=\frac{4-6}{1-0}=\frac{-2}{1} \\ r=-2 \end{gathered}[/tex]The rate is -2.
QUESTION B: Between 1 and 3.
Between 1 and 3, we will use the following parameters to calculate the rate:
[tex]\begin{gathered} x_1=1 \\ x_2=3 \\ y_1=4 \\ y_2=2 \end{gathered}[/tex]Therefore, the rate is:
[tex]\begin{gathered} r=\frac{2-4}{3-1}=\frac{-2}{2} \\ r=-1 \end{gathered}[/tex]The rate is -1.
QUESTION C: Between 3 and 6.
Between 3 and 6, we will use the following parameters to calculate the rate:
[tex]\begin{gathered} x_1=3 \\ x_2=6 \\ y_1=2 \\ y_2=3 \end{gathered}[/tex]Therefore, the rate is:
[tex]\begin{gathered} r=\frac{3-2}{6-3} \\ r=\frac{1}{3} \end{gathered}[/tex]The rate is 1/3.
graph the line with slope 1/3 passing through the point (4,2)
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To graph a line we need two points, to find a second one we need the equation of the line. The equation of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values given we have:
[tex]\begin{gathered} y-2=\frac{1}{3}(x-4) \\ y-2=\frac{1}{3}x-\frac{4}{3} \\ y=\frac{1}{3}x-\frac{4}{3}+2 \\ y=\frac{1}{3}x+\frac{2}{3} \end{gathered}[/tex]Once we know the equation of a line we find a second point on the line, to do this we give a value to x and use the equation to find y. If x=1, then:
[tex]\begin{gathered} y=\frac{1}{3}\cdot1+\frac{2}{3} \\ y=\frac{1}{3}+\frac{2}{3} \\ y=\frac{3}{3} \\ y=1 \end{gathered}[/tex]Then we have the point (1,1).
Now that we have two points of the line we plot them on the plane and join them with a straight line. Therefore the graph of the line is:
Find if -3w - 6(u + 2v) if u = -3j, v = i + 2], and w =combination of unit vectors.-;. Express your answer as a linear
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we have the expressiob
-3w - 6(u + 2v)
where
u=-3j
v=i+2j
w=-(1/3)i-(7/3)j
substitute the given values in the expression
so
-3(-(1/3)i-(7/3)j)-6(-3j+2(i+2j))
(i+7j)-6(-3j+2i+4j)
(i+7j)-6(2i+j)
(i+7j)-12i-6j
answer is
-11i+jJudy has 15 books in her library. She bought several books at a thrift storeon Saturday. She now has 84 books in her library. How many books did shebuy at the thrift store? Write an equation to solve the problem use b forthe variable.
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Let b the number of books Judy has bought.
The given data can be expressed as,
[tex]15+b=84[/tex]Answer:
69 books
15+ b= 84
Step-by-step explanation:
A rectangle has vertices at (-2, 11), (-2,4), (6, 11), and (6, 4). Pablo says the area of the rectangle is 49 square units and his work is shown below. Steps Step 1 Pablo's Work Base: 1- 21+61= 8 Step 2 Step 3 Height: 11-4-7 Area: 8x7=49 square units Where, if at all, did Pablo first make a mistake finding the area of the rectangle? Step 1 Step 2 Step 3
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The result of the calculation of the base is good because the distance between -2 and 6 is 8. The result of the calculation of the height is good because the distance between 4 and 11 is 7. The mistake is seen in the part of the multiplication, because 8x7 is equal to 56 , not 49.
So, the mistake was made when doing the Step 3.
help me please
thank you
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Answer:
(-7, 3)
Step-by-step explanation:
what Since the endpoints of the interval are not included, use parentheses.
what is the answer to 8/8^12
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thanks for the help!!!!!
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The required values of given the trigonometric functions are sin(A + B) = -100/2501 and sin(A - B) = -980/2501.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
We have been given that the trigonometric function
sin (A) = -60/61 and cos(B) = 9/41
So cos (A) = √1 - (-60/61)² = 11/61, and sin(B) = √1 - (9/41)² = 40/41
To compute the trigonometric functions sin(A + B) and sin(A - B)
⇒ sin(A + B) = sinA cosB + cos A sinB
⇒ sin(A + B) = (-60/61)(9/41) + (11/61)(40/41)
⇒ sin(A + B) = -540/2501 + 440/2501
⇒ sin(A + B) = -100/2501
⇒ sin(A - B) = sinA cosB - cos A sinB
⇒ sin(A - B) = (-60/61)(9/41) - (11/61)(40/41)
⇒ sin(A - B) = -540/2501 - 440/2501
⇒ sin(A - B) = -980/2501
Thus, the required values of given the trigonometric functions are sin(A + B) = -100/2501 and sin(A - B) = -980/2501.
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What is the graph of the equation y = 2x + 4?
The y-intercept is which means the line crosses the y-axis at the
). Plot this point.
point
The slope of the line is positive, so it goes
Start at the y-intercept. Move up
0
0 and then move right
). Plot this point.
You are now at the point (
0
Draw a line to connect the two points.
from left to right.
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Answer: 8
Step-by-step explanation: x2 + 4 is 4 x 2
:D
Allied Health - A wound was measured to be 0.8 cm in length. Whaat is the greatest possible error of this weight in grams?
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Ok, so
First of all, we got that the wound was measured to be 0.8cm.
This measurement equals to:
[tex]0.8\operatorname{cm}\cdot\frac{10\operatorname{mm}}{1\operatorname{cm}}[/tex]0.8cm is equal to 8 millimeters.
Now, the greatest possible error in a measurement is one half of the precision (smallest measured unit).
8 mm was measured to the nearest 1 mm, so the measuring unit is 1 mm.
So, one half of the precision (1mm) is 0.5
Therefore, the greatest possible error is 0.5 mm
In the answer section, give the question letter and the word TRUE or FALSE for each of the following:
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a) We rewrite the right side of the expression as:
[tex](-2)^4=((-1)\cdot2)^4=(-1)^4\cdot2^4=1\cdot2^4=2^4\ne-2^4.[/tex]So we see that the expression of point a is FALSE.
b) We consider the expression:
[tex]b^x.[/tex]We take the logarithm in base b, we get:
[tex]\log_b(b^x)=x\cdot\log_b(b)=x\cdot1=x.[/tex]We see that the logarithm of a number x to a base b is just the exponent you put onto b to make the result equal x. We conclude that this expression is TRUE.
c) We know that in any base a, we have:
[tex]\log_a(0)\rightarrow-\infty.[/tex]We conclude that the expression of this item is FALSE.
d) Logarithms are defined only for numbers greater than 0. So we conclude that this expression is FALSE.
e) We consider the expression:
[tex]\log_b(b^{10})-\log_b(1)=10.[/tex]Applying the properties of logarithms, we get:
[tex]\begin{gathered} 10\cdot\log_bb-0=10, \\ 10\cdot1=10, \\ 10=10\text{ \checkmark} \end{gathered}[/tex]We see that this expression is TRUE.
Answera) FALSE
b) TRUE
c) FALSE
d) FALSE
e) TRUE
What is the product in simplest form? State any restrictions on the variable9X^2+9X+18)/(X+2) TIMES (x^2-3x-10)/(x^2+2x-24)
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So, here we have the following expression:
[tex]\frac{9x^2+9x+18}{x+2}\cdot\frac{x^2-3x-10}{x^2+2x-24}[/tex]The first thing we need to notice before simplifying, is that the denominator can't be zero.
As you can see,
[tex]\begin{gathered} x+2\ne0\to x\ne-2 \\ x^2+2x-24\ne0\to(x+6)(x-4)\ne0\to\begin{cases}x\ne-6 \\ x\ne4\end{cases} \end{gathered}[/tex]These are the restrictions on the given variable.
Now, we could start simplyfing factoring each term:
[tex]\begin{gathered} \frac{9x^2+9x+18}{x+2}\cdot\frac{x^2-3x-10}{x^2+2x-24},x\ne\mleft\lbrace2,4,-6\mright\rbrace \\ \\ \frac{9(x^2+x+2)}{x+2}\cdot\frac{(x-5)(x+2)}{(x+6)(x-4)},x\ne\lbrace2,4,-6\rbrace \end{gathered}[/tex]This is,
[tex]9(x^2+x+2)\cdot\frac{(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]So, the answer is:
[tex]\frac{9(x^2+x+2)(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]It could be also written as:
[tex]\frac{(9x^2+9x+18)(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]On a coordinate plane, a parabola with a solid boundary line opens up. It goes through (negative 1, 0), has a vertex at (4, negative 125), and goes through (9, 0). Which inequality in standard form represents the shaded region? y greater-than-or-equal-to x squared + 8 x + 9 y greater-than-or-equal-to x squared minus 8 x minus 9 y greater-than-or-equal-to 5 x squared minus 40 x minus 45 y greater-than-or-equal-to 5 x squared + 40 x + 45
Answers
The inequality represented by the parabola is given as follows:
y ≥ 5x² - 40x -45.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the rule presented as follows:
y = a(x - h)² + k
In which the parameters are described as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.In the context of this problem, the vertex is given by:
(4, -125).
Hence:
y = a(x - 4)² - 125
When x = -1, y = 0, hence the leading coefficient is found as follows:
0 = 25a - 125
25a = 125
a = 125/25
a = 5.
Hence the equation is given as follows:
y = 5(x - 4)² - 125
y = 5(x² - 8x + 16) - 125
y = 5x² - 40x -45.
The inequality has a solid boundary line, hence it contains the equal sign, and the values above the parabola are plotted, hence it is given by:
y ≥ 5x² - 40x -45.
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please help this is for my study guide thanks! (simplify)
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One way of simplifying the given expression is by using the following definition:
[tex]k^{-1}=\frac{1}{k}[/tex]So, for the given expression, we have:
[tex]-3k^{-1}=-3\cdot\frac{1}{k}=-\frac{3}{k}[/tex]Therefore, a possible answer is:
[tex]-\frac{3}{k}[/tex]2. Write an equation of the ellipse with foci at (0, +2) and co-vertices at （+1, 0）.དུ དུའི - 1།14︽ 》སོ – །
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Given,
The foci of the ellipse is (0, +2)(0.-2)
The co vertices of the ellipse is (1, 0)(-1, 0)
The genral equation of ellipse is,
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]The equation of the foci is,
[tex]\begin{gathered} (0,\text{ }\pm c)=(0,\text{ }\pm2) \\ \text{The value of c is 2.} \end{gathered}[/tex]The equation of co vertices is,
[tex]\begin{gathered} (\pm a,\text{ 0)=(}\pm1,\text{ 0)} \\ \text{The value of a is 1.} \end{gathered}[/tex]we know that,
[tex]\begin{gathered} b^2=a^2+c^2 \\ b=\sqrt[]{5} \end{gathered}[/tex]Substituting the value then,
[tex]\begin{gathered} \frac{x^2}{1^2}+\frac{y^2}{\sqrt[]{5}^2}=1 \\ x^2+\frac{y^2}{5}=1 \end{gathered}[/tex]Hence, option d is correct.
A rectangle's base is 2 in shorter than five times its height. The rectangle's area is 115 in². Find this rectangle's dimensions.
The rectangle's height is
The rectangle's base is
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Answer:
The rectangle's height is 5 in,The rectangle's base is 23 in.Step-by-step explanation:
Let the dimensions are b and h.
The area of rectangle is the product of two dimensions.
We have:
b = 5h - 2,bh = 115 in².Solve the equation by substitution:
h(5h - 2) = 1155h² - 2h = 1155h² - 2h - 115 = 05h² - 25h + 23h - 115 = 05h(h - 5) + 23(h - 5) = 0(h - 5)(5h + 23) = 0h - 5 = 0 and 5h + 23 = 0h = 5 and h = - 23/5The second root is discarded as negative.
The height is 5 in,The base is: 5*5 - 2 = 23 inAnswer:
Height = 5 in
Base = 23 in
Step-by-step explanation:
[tex]\boxed{\textsf{Area of a rectangle} = \sf Base \times Height}[/tex]
Let x be the height of the rectangle.
Given values:
Height = x inBase = (5x - 2) inArea = 115 in²Substitute the values into the formula for area and solve for x:
[tex]\begin{aligned}\sf Area & = \sf Base \times Height\\\\115&=x(5x-2)\\115&=5x^2-2x\\5x^2-2x-115&=0\\5x^2-25x+23x-115&=0\\5x(x-5)+23(x-5)&=0\\(5x+23)(x-5)&=0\\\\\implies 5x+23&=0 \implies x=-\dfrac{23}{5}\\\implies x-5&=0 \implies x=5\end{aligned}[/tex]
As length is positive, x = 5.
To find the rectangle's dimensions, substitute the found value of x into the expressions for the height and base:
[tex]\implies \sf Height=5\;in[/tex]
[tex]\begin{aligned}\implies \sf Base&=\sf 5(5)-2\\&=\sf 25-2\\&=\sf 23\;in\end{aligned}[/tex]
