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The angle formed outside the circle by the intersection of a tangent and a secant is equal to half of the difference of the intercepted arcs. The bigger arc is 180º, because the starting point of the secant and the starting point of the tangent are precisely on the opposite position of each other(we can see that by counting the same amount of seats between them on both sides). The smaller arc is equal to 90º, therefore
[tex]w^o=\frac{1}{2}(180^o-90^o)=45^o[/tex]Related Questions
100 points!!!!
PLS WRITE IN SLOPE INTERCEPT FORM
–18y + 8 = 12x
SOLVE FOR Y
Answers
Answer: y = (-2/3)x + (4/9)
Step-by-step explanation:
y = mx + b is the form expected
-18y + 8 = 12x
subtract 8 from both sides
-18y = 12x - 8
divide both sides by -18
y = (12x/-18) - (8/-18)
Simplify the negatives and pull x out of the parenthesis (this only works if x is in the numerator).
y = (-12/18)x + 8/18
Simplify the fractions
y = (-2/3)x + 4/9
Answer:
The required value of y is,
y = -(2/3)x + (4/9)Step-by-step explanation:
Given equation,
→ -18y + 8 = 12x
The slope-intercept form is,
→ y = mx + b
Let's rewrite the equation,
→ y = mx + b
→ -18y + 8 = 12x
→ -18y = 12x - 8
→ -y = (12x - 8)/18
→ -y = (2/3)x - (4/9)
→ y = -(2/3)x + (4/9)
Hence, this is the answer.
Find how many years it would take for an investment of $4500 to grow to $7900 at an annual interest rate of 4.7% compounded daily.
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To answer this question, we need to use the next formula for compound interest:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]From the formula, we have:
• A is the accrued amount. In this case, A = $7900.
,• P is the principal amount. In this case, $4500.
,• r is the interest rate. In this case, we have 4.7%. We know that this is equivalent to 4.7/100.
,• n is the number of times per year compounded. In this case, we have that n = 365, since the amount is compounded daily.
Now, we can substitute each of the corresponding values into the formula as follows:
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow7900=4500(1+\frac{\frac{4.7}{100}}{365})^{365t}[/tex]And we need to solve for t to find the number of years, as follows:
1. Divide both sides by 4500:
[tex]\frac{7900}{4500}=(1+\frac{0.047}{365})^{365t}[/tex]2. Applying natural logarithms to both sides (we can also apply common logarithms):
[tex]\ln \frac{7900}{4500}=\ln (1+\frac{0.047}{365})^{365t}\Rightarrow\ln \frac{7900}{4500}=365t\ln (1+\frac{0.047}{365})[/tex]3. Then, we have:
[tex]\frac{\ln\frac{7900}{4500}}{\ln(1+\frac{0.047}{365})}=365t\Rightarrow4370.84856503=365t[/tex]4. And now, we have to divide both sides by 365:
[tex]\frac{4370.84856503}{365}=t\Rightarrow t=11.9749275754[/tex]If we round the answer to two decimals, we have that t is equal to 11.97 years.
What value of t makes the following equation true?
5t−2=6t−7
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give two-sided of a triangle, find a range of a possible side length of the third side 24 and 52
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For a triangle to be possible with 3 given lengths, the largest side must be lower than the sum of the two remaining sides.
Let L be the length of the third side. There are two cases:
If L is the largest side, then:
[tex]\begin{gathered} L<24+52 \\ \Rightarrow L<76 \end{gathered}[/tex]If L is not the largest side, then the largest side has a measure of 52 and:
[tex]\begin{gathered} 52<24+L \\ \Rightarrow52-24Since both conditions should meet for a triangle to be formed, then:[tex]28Therefore, the range of possible values for L is:[tex]undefined[/tex]coupon A 60% off of $87 pants coupon B $55 rebate on $87 pants
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We are given two coupons A and B. Coupon A gives a 60% discount on a $87 item. Let's calculate the amount to pay by subtracting 60% of 87. We do that by multiplying 87 by 60/100, like this:
[tex]87(\frac{60}{100})=52.2[/tex]Now we subtract this from the initial price, like this:
[tex]87-52.2=34.8[/tex]therefore, using coupon A she must pay $34.8
For coupon B there's a rebate of $55. We calculate the amount to pay by subtracting 55 to the total price of 87, like this:
[tex]87-55=32[/tex]Therefore, using coupon B she must pay $32.
Coupon B gives the lowest price, the price of coupon B compared to coupon A is calculated by subtracting both prices:
[tex]34.8-32=2.8[/tex]Therefore, with coupon B she pays $2.8 less than the price with coupon A.
I have a practice problem in the calculus subject, I’m having trouble solving it properly
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The limit of a function is the value that a function approaches as that function's inputs get closer and closer to some number.
The question asks us to estimate from the table:
[tex]\lim _{x\to-2}g(x)[/tex]To find the limit of g(x) as x tends to -2, we need to check the trend of the function as we head towards -2 from both negative and positive infinity.
From negative infinity, the closest value we can get to before -2 is -2.001 according to the values given in the table. The value of g(x) from the table is:
[tex]\lim _{x\to-2^+}g(x)=8.02[/tex]From positive infinity, the closest value we can get to before -2 is -1.999 according to the values given in the table. The value of g(x) from the table is:
[tex]\lim _{x\to-2^-}g(x)=8.03[/tex]From the options, the closest estimate for the limit is 8.03.
The correct option is the SECOND OPTION.
An isosceles right triangle has 6 cm legs . Find the length of the hypotenuse
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Step-by-step explanation:
we have a right-angled triangle.
so, we can use Pythagoras
c² = a² + b²
c is the Hypotenuse, a and b are the legs.
in our case
c² = 6² + 6² = 36 + 36 = 72
c = Hypotenuse = sqrt(72) = 8.485281374... cm
Answer:
hypotenuse = √72 (or 8.49)
Step-by-step explanation:
An isosceles right triangle has 6 cm legs . Find the length of the hypotenuse
isosceles right triangle = 2 equal side and 2 equal angleswe use the Pythagorean theorem (In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides)hypotenuse² = 6² + 6²
hypotenuse² = 36 + 36
hypotenuse² = 72
hypotenuse = √72 (or 8.49)
can you please help me. I am running out of time and I really need this grade.
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A system of equations is consistent if the system has a solution and it is inconsistent if it has no solution.
Since the lines intersect at a point, the system has a solution and the solution is unique.
If a system has a unique solution, then the system is independent.
Therefore, the given system of equations is consistent and independent. It has a unique solution.
Triangle DEF is rotated 60⁰ clockwise about the vertex to obtain triangle LMN. if the m
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EXPLANATION
The measure of the angle LMN is equal to 40 degrees, then the measure of the angle LMN is the same because the rotation does not modify the angle.
If the area of a rectangular field is x2 – 3x + 4 units and the width is 2x – 3, then find the length of the rectangular field.x2- 3 x + 42 x − 3 unitsx2 - 3x + 4 units2x - 3 units3x + 4 units
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Solution
We are given the following
[tex]\begin{gathered} Area=x^2-3x+4 \\ \\ Width=2x-3 \\ \\ Length=? \end{gathered}[/tex]Using the Area of a Rectangle we have
[tex]\begin{gathered} Area=lw \\ \\ l=\frac{A}{w} \\ \\ l=\frac{x^2-3x+4}{2x-3} \end{gathered}[/tex]Therefore, the answer is
[tex]\frac{x^{2}-3x+4}{2x-3}units[/tex]What should you do to finish solving this equation?6y + 4y + 90 = 36010y + 90 = 360Add 90 then divide by 102 subtract 90 then multiply by 10Add 10 then multiply by 904Subtract 90 then divide by 10O 102O 304h
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answer is substract 90 then divide by 10
Simplify cot(t)/csc(t)-sin(t) to a single trig function
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The single trig function that simplifies the function is sec(t)
How can we simplify the function?Trigonometry deals with the functions of angles and how they're applied.
Given cot(t)/csc(t)-sin(t)
since csc(t) = 1/sin(t) , we have:
[tex]\frac{ cot(t)}{csc(t)-sin(t)} = \frac{cot(t)}{\frac{1}{sin(t)} - sin(t) }[/tex]
[tex]\frac{ cot(t)}{csc(t)-sin(t)} = \frac{cot(t)}{\frac{1-sin^{2}(t) }{sin(t)} }[/tex]
since:
cos²(t) = 1 - sin²(t)
Therefore we have:
cot(t) / csc(t)-sin(t) = cot(t)/ cos²(t)/sin(t)
cot(t) / csc(t)-sin(t) = cot(t) / cos(t).cos(t)/sin(t)
Since cos(t) / sin(t) = 1/tan(t) = cot(t)
Therefore:
cot(t) / csc(t)-sin(t) = cot(t)/ cot(t)×cos(t)
cot(t) / csc(t)-sin(t) = 1/cos(t)
Since 1/cost = sec(t)
Finally, cot(t) / csc(t)-sin(t) is sec(t).
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Use the fact that 521•73=38, 033.Enter the exact product of 5.21•7.3
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Answer: 38.033
5.21 x 7.3
= 38.033
Which number line shows the solutions to x > 5? O A. A. 3642 8 2 4 6 8 B. 8 -6 -4 -2 0 2 4 6 8 c. -6-4 2 0 2 4 6 8 D. 8 8 4 2 0 2 4 6 8
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The answer is option C.
thats where there are intergers greater than 5.
If two lines intersect and one of the angles formed has a measure of 67°, which of the following statements are true? Explain your answers.
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Intersecting Lines
When two lines intersect, four angles are formed at the point of intersection.
Two pairs of angles are vertical, i.e., they have the same measure.
Two pairs of angles are complementary (or linear) therefore their sum adds up to 180°.
We are given one of the angles that has a measure of 67°.
Then, another angle also measures 67° (the vertical peer).
One of the other angles is 180° - 67° = 113°
The other angle also measures 113° (the other vertical peer).
According to the facts found above, the following statements are true:
* Vertical angles are congruent, therefore another angle must equal 67°
* The lines form linear pairs
* The lines form complementary angles
* Two of the angles formed measure 113°
* Two of the angles formed will have a sum of 180°
Note: The last statement should read "Two pairs of angles formed..."
What fraction is bigger 25/5 or 24/6?
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Olivia goes out to lunch. The bill, before tax and tip, was $13.90. A sales tax of 6% was added on. Olivia tipped 23% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.
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According to the information given in the exercise, the bill before the tax and tip was $13.90 and the sales tax of 6% was added to that amount.
By definition, you can write 6% as a Decimal number by dividing it by 100. Then, this is:
[tex]\frac{6}{100}=0.06[/tex]Let be "t" the amount (in dollars) of the sales tax.
To find the value of "t", you can set up the following equation:
[tex]t=(13.90)(0.06)[/tex]Finally, evaluating, you get that this is:
[tex]t=0.834[/tex]Rounded to the nearest cent, this is:
[tex]t\approx0.83[/tex]The answer is: $0.83
The length of a rectangle is 6 cm more than the width. If the perimeter is 52 cm. What are the dimensions of the rectangle?
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LA rectangle has two pairs of sides of the same length. If we call W to the width of the rectangle, we know that the length is 6cm more. If we call L the length of the rectangle:
[tex]L=W+6[/tex]The perimeter of a rectangle is twice the length plus twice the width:
[tex]Perimeter=2L+2W[/tex]Since we know that the perimeter is 52 cm, we can write the system of equations:
[tex]\begin{cases}L={W+6} \\ 2L+2W=52{}\end{cases}[/tex]We can substitute the first equation into the second one:
[tex]2(W+6)+2W=52[/tex]And solve:
[tex]2W+12+2W=52[/tex][tex]\begin{gathered} 4W=52-12 \\ . \\ W=\frac{40}{4}=10\text{ }cm \end{gathered}[/tex]We know that W = 10cm, we can now find L:
[tex]L=10+6=16\text{ }cm[/tex]Thus, the dimensions of the rectangle are:
Length: 16 cm
Width: 10 cm
Can you please help me out with the a question
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Arc XY = 2π • (PX)/ 4
. = 2π • 5/4
. = 6.28 • 5/4= 31.40/4 = 7.85
Then answer is
Option G) 7.854
9) Write an equation of a line that is steeper than y- 6x + 2
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The distance around a water fountian is 150 inches what is the distance from the edge of the fountian to the center
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Answer:
The distance from the edge of the fountain to the centre is approximately 23.87 inches.
The water fountain forms a circle. The distance around the water fountain is the circumference of the circle formed.
Therefore,
circumference = 2πr
150 = 2πr
The distance from the edge of the fountain to the centre is the radius of the circle formed. Therefore,
75 = πr
r = 75 / 3.14159
r = 23.8732616287
r = 23.87 inches
The distance from the edge of the fountain to the centre is approximately 23.87 inches.
Last year, Kevin had $10,000 to invest. he invested some of it in an account that paid 6% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. after one year, he received a total of $920 in interest. how much did he invest in each account?first account:second account:
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Simple interest is represented by the following expression:
[tex]\begin{gathered} I=\text{Prt} \\ \text{where,} \\ I=\text{ interest} \\ P=\text{principal} \\ r=\text{interest rate in decimal form} \\ t=\text{ time (years)} \end{gathered}[/tex]We need to create a system of equations:
Let x be the money invested in the account that paid 6%
Let y be the money invested in the account that paid 10%
So, he received a total of $920 in interest, then:
[tex]920=0.06x+0.1y\text{ (1)}[/tex]And we know that money invested must add together $10,000:
[tex]x+y=10,000\text{ (2)}[/tex]Then, we can isolate y in equation (2):
[tex]y=10,000-x[/tex]Now, let's substitute y=10,000-x in the equation (1):
[tex]\begin{gathered} 920=0.06x+0.1(10,000-x) \\ 920=0.06x+1000-0.1x \\ 0.1x-0.06x=1,000-920 \\ 0.04x=80 \\ x=\frac{80}{0.04} \\ x=2,000 \end{gathered}[/tex]That means, he invested $2,000 in the account that paid 6% simple interest. Now, having x, we are going to substitute x in the second equation (2):
[tex]\begin{gathered} y=10,000-x \\ y=10,000-2,000 \\ y=8,000 \end{gathered}[/tex]He invested $8,000 in the account that paid 10% simple interest per year.
nd the Geometry meand of 4 and 15.
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we know that
the geometric mean is the product of all the numbers in a set, with the root of how many numbers there are
so
In this problem we have two numbers
so
the geometric mean is equal to
[tex]\begin{gathered} \sqrt[=]{4\cdot15} \\ \sqrt[]{60} \\ 2\sqrt[]{15} \end{gathered}[/tex]find the missing lenghts, the triangle in each pair are similar.
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Since the triangles are similar, we have that
[tex]\frac{50}{40}=\frac{x}{52}[/tex]then
[tex]x=\frac{52\times50}{40}=65[/tex]then the answer will be D) 65many solutions can be found for the system of linear equations represented on the graph?A. no solution B. one solution C. two solution D. Infinity many solutions
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The lines are not intersecting. The system of linear equations has a solution only if the lines corresponding to the equations intersect.
The general linear equation is,
y=mx+c, where m is the slope.
The slopes of lines m=2.
Since the graphs are parallel or have the same slope and will never intersect, the system of linear equations have no solution.
Do you know anything about dilation!?
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Deter mine the intervals for which the function shown below is increasing
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Answer:
The interval at which the function is increasing is from x = -2 to x = 0. In interval notation, it is (-2, 0).
Explanation:
See the graph below for the pattern of the function.
As you can see above, from x = -∞ until x = -2, the value of the function decreases from y = +∞ to y = -7.
Then, starting at x = -2 to x = 0, the value of the function increases from y = -7 to y = -3.
Lastly, starting at x = 0 to +∞, the value of the function decreases again from y = -3 to -∞.
Hence, the interval at which the function is increasing is at (-2, 0).
Evaluate 7a - 5b when a = 3 and b = 4 .
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In a sourball game, a fizzy is worth 2 points and a X is worth 5 points. K and W recently played for the sourball game. During the game, K scored eight more fizzles than the W, but scored 5 fewer Y than the W. Together the two teams scored 93 pints total. What was the final score?
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Using mathematical operations of addition, multiplication, division, and subtraction, the final score was:
K = 42 pointsW = 51 points.What are mathematical operations?The basic mathematical operations for getting mathematical results from numbers, values, and variables include addition, multiplication, division, and subtraction.
In this situation, we apply these four basic mathematical operations.
Fizzy = 2 points
X = 5 points
Total scores = 93 points
The points in 8 Fizzys = 16 points (8 x 2)
The points in 5 Xs = 25 points (5 x 5)
The equation showing the total scores of K = total scores + 16 - 25
= (93 + 16 - 25)/2
= 42 points
The equation showing the total scores of W = total scores - 16 + 25
= (93 - 16 + 25)/2
= 51 points
Final scores are K = 42 and W = 51.
Thus, applying mathematical operations, the final score shows that K scored 42 points while W scored 51 points, totaling 93 points for the two teams.
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A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his weekly rate of eating the cake?
5
36
35
36
cakes/week
cakes/week
1
1 cakes/week
35
01. cakes/week
4
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Answer:
11.2 Slices / Week
Step-by-step explanation:
We know that Jake has eaten 5 slices of cake in 3 days. You can divide 5 / 3 to get an average of 1.6 slices of cake being eaten per day. The question asks what the weekly rate or eating the cake will be, do you need to multiple 1.6 x 7 for the total amount of cake eaten per week, which is 11.2 slices!
Answer:
11.6
explanation
we have 7 days.
7days-3days =4
in 3 days he has eaten 5 slices
again 4-3 days=1
so in 6 days he has eaten 10 slices
we have 1 day left.so if he eats 5 slices in 3 day,how many he eat slices in 1 day?5/3=1.6
10+1.6=11.6