4. 1st drop down answer A. 90B. 114C. 28.5D. 332nd drop down answer choices A. Parallel B. Perpendicular 3rd drop down answer choices A. 180 B. 360 C. 270D. 90 4th drop down answer choices A. 33B. 57C. 90D. 28
Answers
Answer:
Tangent to radius of a circle theorem
A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent.
Part A:
With the theorem above, we will have that the tangent is perpendicular to the line radius drawn from the point of tangency
Therefore,
The value of angle CBA will be
[tex]\Rightarrow\angle CBA=90^0[/tex]Part B:
Since the angle formed between the tangent and the radius from the point of tangency is 90°
Hence,
The final amswer is
Tangent lines are PERPENDICULAR to a radius drawn from the point of tangency
Part C:
Concept:
Three interior angles of a triangle will always have the sum of 180°
Hence,
The measure of angles in a triangle will add up to give
[tex]=180^0[/tex]Part D:
Since we have the sum of angles in a triangle as
[tex]=180^9[/tex]Then the formula below will be used to calculate the value of angle BCA
[tex]\begin{gathered} \angle ABC+\angle BCA+\angle BAC=180^0 \\ \angle ABC=90^0 \\ \angle BAC=57^0 \end{gathered}[/tex]By substituting the values,we will have
[tex]\begin{gathered} \operatorname{\angle}ABC+\operatorname{\angle}BCA+\operatorname{\angle}BAC=180^{0} \\ 90^0+57^0+\operatorname{\angle}BCA=180^0 \\ 147^0+\operatorname{\angle}BCA=180^0 \\ substract\text{ 147 from both sides} \\ 147^0-147^0+\operatorname{\angle}BCA=180^0-147^0 \\ \operatorname{\angle}BCA=33^0 \end{gathered}[/tex]Hence,
The measure of ∠BCA = 33°
Related Questions
(2, -3) (4, -2)
Slope intercept
Answers
The slope of the given coordinates is m = 1/2.
What is the slope?A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the point where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.So, the slope of (2, -3) (4, -2):
The slope formula: m = y₂ - y₁/x₂ - x₁Now, solve for slope by putting the values as follows:
m = y₂ - y₁/x₂ - x₁m = -2 - (-3)/4 - 2m = -2 + 3/2m = 1/2Therefore, the slope of the given coordinates is m = 1/2.
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The correct question is shown below:
Find the slope using the coordinates (2, -3) (4, -2).
4 Consider the quadratic equation below.[tex]4 {x}^{2} - 5 = 3x + 4[/tex] Determine the correct set-up for solving the equation using the quadratic formula.
Answers
The equation:
4x² - 5 = 3x + 4
First, we need to re-arrange in the form : ax² + bx + c
4x² - 5 = 3x + 4
4x² - 3x -5 -4 = 0
4x² - 3x -9 =0
comparing the above with ax² + bx + c
a= 4 b= -3 c=-9
we will then substitute the values into the quadratic formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(4)(-9)}}{2(4)}[/tex]if Em=11, Am=16,CF=27, What are the lengths of the following sides
Answers
We will have the following:
First, we calculate AE as follows:
[tex]AE=\sqrt[]{AM^2-EM^2}[/tex]Now, we replace values and solve it:
[tex]AE=\sqrt[]{16^2-11^2}\Rightarrow AE=3\sqrt[]{15}[/tex]From theorem AE = EC therefore EC = esqrt(15); so, the following is true:
[tex]AC=AE+EC\Rightarrow AC=2AE\Rightarrow AC=2(3\sqrt[]{15})\Rightarrow AC=6\sqrt[]{15}[/tex]Knowing this, we then determine FA as follows:
[tex]FA=\sqrt[]{AC^2-CF^2}[/tex]We then determine BE, DM & CM as follows:
Covert1 1/4 percent to a decimal 5 bill has received a wage increased. His new hourly wage is $14.30 compared to previous wage of $12.95 find the percentage increase in bill hourly wage. Round it off to 2 decimal places
Answers
The percentage increase in bill hourly wage is 10.42%
Given,
Bill has received a wage increased.
His new hourly wage is $14.30
and, compared to old wage of $12.95
To find the percentage increase in bill hourly wage.
Now According to the question:
New bill is = $14.30
Old bill is = $ 12.95
= ($14.30 - $12.95) / $12.95
= $1.35 / $12.95
= 10.42%
Hence, The percentage increase in bill hourly wage is 10.42%
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need help please 16x=-44-4y
-8x=28+4y
Answers
Answer: (x,y)= (-2/5,-43/5)
Step-by-step explanation:
I need help with system B. I have one right. And if the answer is infinitely. It asks to satisfy and it has Y=
Answers
We have the next system of equations
[tex]\begin{gathered} -5x-y=5 \\ -5x+y=5 \end{gathered}[/tex]We can sum both equations we can eliminate one variable
[tex]\begin{gathered} -10x=10 \\ \end{gathered}[/tex]then we isolate the x
[tex]x=\frac{10}{-10}=-1[/tex]Therefore x=-1 then we substitute the value of x in order to find the value of y in the second equation
[tex]-5(-1)+y=5[/tex]Then we simplify
[tex]5+y=5[/tex]Then we isolate the y
[tex]y=5-5[/tex][tex]y=0[/tex]ANSWER
x=-1
y=0
12x=8x+1 what is the answer
Answers
The answer of the given equation is x = 1/4 or 0.25
We are given the equation:-
12x = 8x + 1
We have to solve the equation to find the value of x.
Rearranging the equation to get the like terms on the same side, we get,
12x - 8x = 1
4x = 1
x = 1/4
Hence, the value of x is 1/4 or 0.25.
Like terms
Like terms can be defined as terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only we can combine like terms.
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When water flows across farmland, some of the soil is washed away, resulting in erosion. Researchers released water
across a test bed at different flow rates and measured the amount of soil washed away. The following table gives the
flow (in liters per second) and the weight (in kilograms) of eroded soil:
Answers
The correlation coefficient between flow rate and amount of eroded soil is:
0.967.
Correlation coefficientsThe correlation coefficient is an index that measures correlation between two variables, assuming values between -1 and 1.
If it is positive, the relation is positive, meaning that the variables are direct proportional. If it is negative, the variables are inverse proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the variables is strong.
Given a data-set of two points, the correlation coefficient is found inserting points of the data-set into the calculator. In this problem, the points in the data-set are given as follows:
(0.31, 0.82), (0.85, 1.95), (1.26, 2.18), (2.47, 3.01), (3.75, 6.07).
Using a calculator, the coefficient is given as follows:
0.967.
Hence the last option gives the correct coefficient.
Missing informationThe complete problem is given by the image at the end of the answer.
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12) A row of roses is planted in a repeating pattern of "red, red, yellow, yellow, pink, pink
There is a total of 56 roses planted in the row. How many red roses are there?
Answer:
********
Answers
Answer:
22
Step-by-step explanation:
XXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXX
Each of the capital X's are red roses, and there are 56 x's in total.
the number of regular telephones in use is how many times the number of cellular phones? 45% regular phones15% cellular phones6% others34% Cordless phones
Answers
Solution
For this case we have the following info:
45% regular phones
15% cellular phones
6% others
34% Cordless phones
We know that the total regular of phones is 45% and the total of cellular phones are 15% then we can find the ratio like this:
45/15 = 3
Find the time it would take for the general level of prices in the economy to double at an average annual inflation rate of 4%. The doubling time is aboutyears.
Answers
The doubling time for the general price levels in the eonomy given the average annual inflation rate is 18 years.
What is the doubling time?Inflation is a period where the general price levels in an economy rise persistently. When there is an inflation, the prices of goods and services increase. Inflation can either be as a result of an increase in the cost of production or an increase in the demand of a good.
The rule of 72 can be used to determine the doubling time. The rule of 72 is a rule of thumb that determines the number of years it would take an investment to double given its rate of growth.
The rule of 72 = 72 / inflation rate
72 / 4 = 18 years
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What is the simplified expression for the expression below?7(x - 4) - 3(x + 5) A. 4x - 43 B. 4x + 1C. 4x - 13D. 4x - 9
Answers
Answer:
4x - 43
Step-by-step explanation:
This Question requires the concept of solving algebraic expressions.
Algebraic ExpressionsAlgebraic Expressions are expressions made up of alphabet variables and numbers and can be simplified using order of operations just like numerical expressions.
Example: 8(4x-6) = 32x - 48
ApplicationFor this question, we will use the same concept as above to solve for the expression.
[tex]7(x - 4) - 3(x + 5) = 7x - 28 - (3x + 15) \\ = 7x - 28 - 3x - 15 \\ = 4x - 43[/tex]
What is the unknown angle b?
Answers
Answer:
48°
Explanation:
A line always equals 180°. The angle on the right is a 90° angle (we know this because or the little red box shown) and the angle in the middle is 42°. We would add 42° and 90° to get the combination of both which is 132°
42+90=132
Then subtract 132° from 180° to find unknown angle b.
180-132=48
Unknown angle b= 48°
Find the percent change to the nearest percent for the function following
f(x) = 3(1 -.2)^-x
Answers
The percentage change of the function given in the task content as required is; 20%.
Percent change in exponential functions.It follows from the task content that the percentage change of the function is to be determined.
The percentage change in exponential functions is represented by the change factor, an expression on which the exponent is applied.
On this note, since the function given is an exponential function in which case, the change factor is; (1 - .2).
It consequently follows that the change implies a 20% decrease. This follows from the fact that 20% is equivalent to; 0.2.
Ultimately, the percentage change of the function is; 20%.
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Dolphin 1 dove 200 feet underwater. Dolphin 2 dove 30% farther. After dolphin 2 dove down, it ascended 25 1/2 feet, then descended 40 1/2 feet. How far under the water is the dolphin?
Answers
Data:
Dolphin 1: 200ft
Dolphin2:
30% farther: 200ft+60ft=260ft
-Find the 30% of 200
[tex]200\cdot\frac{30}{100}=60[/tex]Ascende 25 1/2 feet and then descended 40 1/2 feet:
Substract to the initial 260ft the 25 1/2 ft and add 40 1/2:
[tex]260-25\frac{1}{2}+40\frac{1}{2}[/tex]To sum or substract mixed numbers write it as fractions:
[tex]\begin{gathered} 25\frac{1}{2}=\frac{50}{2}+\frac{1}{2}=\frac{51}{2} \\ \\ 40\frac{1}{2}=\frac{80}{2}+\frac{1}{2}=\frac{81}{2} \end{gathered}[/tex]Then You have:
[tex]260-\frac{51}{2}+\frac{81}{2}[/tex]You can also write the 260 as a fraction with the same denominator (2):
[tex]\begin{gathered} \frac{520}{2}-\frac{51}{2}+\frac{81}{2} \\ \\ =\frac{520-51+81}{2}=\frac{550}{2}=275 \end{gathered}[/tex]Then, the dolphin 2 is 275 feet under the waterDISREGARD THE LAST ONE
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
A company manufactures computer memory chips as circular silicon wafers with a diameter of 10 Inches. The wafers are cut into
different sized sectors. Match each wafer's central angle to the area of that sector.
48°
20°
62°
45°
55°
Answers
Answer:
25/18 - 20
155/36 - 62
25/8 - 45
Step-by-step explanation:
Solve the inequality for x and identify the graph of its solution.|x+ 2] < 2Choose the answer that gives both the correct solution and the correct graph.
Answers
| x + 2 | < 2
-2 < x + 2 < 2
-2 - 2 < x + 2 < 2 - 2
-4 < x < 0 This is the inequality
Letter B is the right choice.
How does a graph of quadratic function (f(x) = ax2 + bx + c) vary when the a,b, c changes from -1 to +1?
Answers
When a, b, c changes from -1 to +1, the parabolas opens and widens.
Given,
The quadratic function, f(x) = ax² + bx + c
We have to find the change in graph when a, b, c changes from -1 to 1.
First lets consider:
a and b as constants and c is varying.
That is,
x² + x + c
Then, the parabola will move up and down.
Now, lets consider:
a and c as constants and b is varying.
That is,
x² + bx + 1
Then, the vertex will move but all parabolas passes through the points (0, c)
Now, we can move to the question.
What happens to graph when +1 changes to -1.
So,
b and c should keep constant and a is varying.
Then,
ax² + x + 1
Here, the parabolas opens and widens.
That is,
When a, b, c changes from -1 to +1, the parabolas opens and widens.
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Generate equivalent expressions using properties of operations. 15-(x•9) what do I need to do
Answers
Given the expression:
15 - (x • 9)
Let's simplify the expression.
To generate an expression equivalent to the given expression, simplify the expression inside the parentheses.
Thus, we have:
[tex]15-9x[/tex]ANSWER:
[tex]15-9x[/tex]
If 10 = 1+4, then 1+9= 10substitution property symmetric property transitive propertyreflexive property8*1=8Multiplicative InverseMultiplicative IdentityMultiplicative Property of ZeroAdditive Identity Property
Answers
Reflexive Property
In Math, especially in geometry, but also in other fiels.
What we have here is the Reflexive Property, that states that
If a= b+c then b+c=a
Multiplicative Identity
The multiplicative identity is the number 1, so every number times 1 is equal to itself and this property is called multiplicative identity.
Four friends had dinner at a restaurant. The bill was $45.40, and they added a 20% tip. The 4 friends shared the total cost equally. How much money did each person pay?
Answers
Answer:
$13.62
Step-by-step explanation:
To find the tip of 20%, multiply 45.40 by 0.20, and you get 54.48.
Now, since there are 4 friends, divide the amount by 4.
54.48/4=13.62
So each person would pay $13.62.
Hope this helps! :D
I need help on number 14!!! Please help and justify your answer!! PLEASE
Answers
as the rate of company B is greater, the company B will reach the top first
Explanationto solve this we can find the rate of each company and then compare
let
[tex]rate=\frac{finished\text{ length of construction}}{time\text{ taken}}[/tex]so
Step 1
convert the mixed number into fractions
remember how
[tex]a\frac{b}{c}=\frac{(a*c)+b}{c}[/tex]so
[tex]\begin{gathered} 5\text{ }\frac{1}{2}=\frac{(5*2)+1}{2}=\frac{11}{2} \\ 3\text{ }\frac{1}{2}=\frac{(3*2)+1}{2}=\frac{7}{2} \end{gathered}[/tex]Step 2
Find the rate of each company
A) Company A
replace
[tex]\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_A=\frac{550}{\frac{11}{2}}=\frac{1100}{11}=100\text{ ft per month} \end{gathered}[/tex]B) Company B
[tex]\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_B=\frac{385}{\frac{7}{2}}=\frac{770}{7}=110\text{ ft per month} \end{gathered}[/tex]Step 3
finally, compare
[tex]\begin{gathered} 110\text{ ft per month }>100\text{ ft per month} \\ hence \\ rate_B>rate_A \end{gathered}[/tex]as the rate of company B is greater, the company B will reach the top first
evaluate each limit. this is in the topic of jump discontinuities.
Answers
we have
[tex]\begin{gathered} \lim _{x\to-2}-x^2-4x-5 \\ \lim _{x\to-2}-(-2)^2-4(-2)-5 \\ \lim _{x\to-2}-4^{}+8-5 \\ \lim _{x\to-2}--1 \end{gathered}[/tex][tex]\lim _{x\to-2}-1=-1[/tex]therefore
the answer is -1When you start your career, you decide to set aside $500 every quarter to deposit into an investment account. The investment firm claims that historically their accounts have earned an annual interest rate of 10.0% compounded quarterly. Assuming this to be true, how much money will your account be worth after 25 years of depositing and investing? Round your answer to the nearest cent. Do not include labels or units. Just enter the numerical value.
Answers
Given:
The principal amount = $500
Interest rate = 10% quarterly
Required:
Find the deposing amount after 25 years.
Explanation:
The amount formula when the interest is compounded quarterly is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where r = interest rate
t = time period
n = The number of compounded times
The amount after 25 years is:
[tex]\begin{gathered} A=500(1+\frac{0.1}{4})^{4\times25} \\ A=500(1+.025)^{100} \\ A=500(1.025)^{100} \end{gathered}[/tex][tex]\begin{gathered} A=500\times11.81371 \\ A=5906.8581 \end{gathered}[/tex]Final Answer:
The amount after 25 years will be &5906.85
Consider right triangle PQR what is the value of tan(R)
6/8
8/10
8/6
10/6
Answers
The value of tan(R) in the right triangle PQR where Perpendicular=QP, Base=RQ, Tan R=P/B. The slope of a straight line is the tangent of the angle made by the line with the positive x-axis.
What is perpendicular?Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular symbol,⟂, can be used to graphically represent the condition of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.
What is base?The base of a right angle triangle is the side on which it is positioned. The calculation can also be done using any of the two sides other than the hypotenuse as the base. It is the side of the right-angled triangle that is perpendicular to its base.
here,
Perpendicular=QP
Base=RQ
Tan R=P/B
=QP/RQ
Tan R=6/8
The perpendicular QP, base RQ, and tan's (R) values in the right triangle PQR. Tan's (R) = P/B. The tangent of the angle formed by the line with the positive x-axis is what determines a line's slope.
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Clarence is saving money to buy a skateboard that costs $97.50. He has $15.05 already saved and plans to save $5.50 each week from his allowance. He also earns $15.60 every two weeks for walking dogs. Suppose Clarence wants to spend some of the money from walking dogs on other things. To the nearest dollar, how much would he need to save from walking dogs each week in order to buy the skateboard 4 weeks earlier than if he just saves his allowance?
Please explain. Thanks!
Answers
Answer:88
Step-by-step explanation:
solve for y please and thank uou
Answers
Similar triangles are triangles that maintain the same ratio even though they are of different scales. Their angles are however equal.
In this case, y is the longest side in triangle 2 as 37.5 is the longest side in triangle 1
The ratio is thus:
[tex]\frac{y}{37.5}=\frac{16.5}{27.5}[/tex]Cross multiplying, we have:
[tex]\begin{gathered} 27.5y\text{ =37.5 x 16.5} \\ to\text{ get y, we divide both sides by 27.5} \\ \frac{27.5y}{27.5}\text{ = }\frac{\text{37.5 x 16.5}}{27.5} \end{gathered}[/tex]y = 22.5
Find the length of the given side for the congruent triangles ABC and A'B'C'.
The length of side AC
The length of side AC is ____.
Answers
ABC and A'B'C' are congruent triangle. The length of the side AC is 5.31cm.
congruent triangle - Congruent triangles are those whose two sides and included angle match those of another triangle's matching sides and angle.
rules -
Each of the three sides is equal.A comparable side and two angles share the same properties.The angle between the two sides is also equal, and there are two equal sides.(given)
AB = 17 cm
BC = 34 cm
Using the trigonometric functions
cos x = B/H
cos(81°) = B/34
B = Cos(81°) x 34
B = 5.31.
ABC and A'B'C' are congruent triangle. The length of the side AC is 5.31cm.
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#8 iOrder the figures described below according to their volumes from least (on top) to greatest (on bottom).= a cylinder with 2-inch radius and 6-inch height= a cube with side length 4 inches= a rectangular prism with a length of 2 inches, a width of 3 inches, and a height of 6 inches
Answers
step 1
Find out the volume of each figure
Cylinder
The volume of a cylinder is given by
[tex]\begin{gathered} V=\pi r^2h \\ V=(3.14)(2)^2(6) \\ V=75.36\text{ in}^3 \end{gathered}[/tex]Cube
The volume of the cube is given by
[tex]\begin{gathered} V=b^3 \\ V=4^3 \\ V=64\text{ in}^3 \end{gathered}[/tex]Rectangular prism
The volume of the prism is given by the formula
[tex]\begin{gathered} V=L*W*H \\ V=(2)(3)(6) \\ V=36\text{ in}^3 \end{gathered}[/tex]therefore
The answer is
rectangular prismcubecylinderWrite a formula for the function obtained when the graph is shifted as described. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!f(x)=x^2 is shifted up 1 unit and to the left 2 units.The new equations f(x)=Answer
Answers
Given the function f(x) defined as:
[tex]f(x)=x^2[/tex]We need to obtain the graph after performing two shifts: 1 unit up and 2 units left. For the first shift, we do the transformation:
[tex]f(x)\rightarrow f(x)+1[/tex]Now, for the second shift:
[tex]f(x)\rightarrow f(x+2)[/tex]Combining these transformations:
[tex]\begin{gathered} f(x)\rightarrow f(x+2)+1 \\ \therefore f(x)=(x+2)^2+1 \end{gathered}[/tex]