Line AC is tangent to circle O at point C
What is the measure of OAC?
The measure of m<OAC is 45degrees
Tangent line to a circleFrom the given diagram, we can see that the line A is tangential to the circle at point C, hence m<C = 90 degrees
Taking the sum of angle in a triangle
m<OAC + 45 + 90 = 180
m<OAC = 180 - 135
m<OAC = 45 degrees
Hence the measure of m<OAC is 45degrees
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If x + 2 has a value of 5 then which of the following is the value of X(x+2)+3(x+2)
The solution of the equation "[tex]x(x+2)+3(x+2)[/tex]" will be "[tex]5(x+3)[/tex]".
According to the question,
[tex]x(x+2)+3(x+2)[/tex]and,
[tex]x+2=5[/tex]By substituting "5" in place of "(x+2)" in the above given equation i.e.,
[tex]x(x+2)+3(x+2)[/tex], we get
= [tex]x(x+2)+3(x+2)[/tex]
= [tex]x(5)+3(5)[/tex]
By applying multiplication, we get
= [tex]5x+15[/tex]
= [tex]5(x+3)[/tex]
Thus the response above is appropriate.
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You have $9, one of your friends has $10, and two of your other friends each have $13. you combine your money to buy arcade tokens. you use a coupon to buy 8 tokens for $1. the cost of the remaining tokens is four for $1. you and your friends share the tokens evenly. how many tokens does each person get? each person gets 65 tokens.
The required number of tokens distributed in each of them is 46 tokens.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Total money = 9 + 10 + 13 + 13 = $45
Total number of persons = 4
For the first $1 there are 8 token
And after that cost of 4 tokens is $1,
Total tokens = 8×1 + 4×(45 - 1)
Total tokens = 8 + 176
Total tokens = 184
Now,
Distribution among the fours,
= 184 / 4
= 46 tokens
Thus, the required number of tokens distributed in each of them is 46 tokens.
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Which expression has an estimated product of 45?
Answer with explanation:
We have to find that expression , which has an estimated product of
1.→44.7 x 2.1
2.→7.5 x 8.4
3.→8.7 x 5.28
4.→38.1 x 7.3
We will start from option 1.
→44.7 x 2.1
44.7 when estimated to nearest tenth=45
2.1, when estimated to nearest tenth=2
44.7 × 2.1=45×2=90
Option 2
7.5 x 8.4
7.5 when estimated to nearest tenth=8
8.4, when estimated to nearest tenth=8
⇒7.5 × 8.4=8×8=64
Option 3
8.7 × 5.28
8.7, when estimated to nearest tenth=9
5.28, when estimated to nearest tenth=5
⇒8.7 × 5.28=9×5=45
Option D
38.1 × 7.3
38.1 when estimated to nearest tenth=38
7.3, when estimated to nearest tenth=7
⇒38×7=266
Option C:⇒8.7 × 5.28 has an estimated product of 45
Solve 2x2 + x − 4 = 0.
x^2 + ____x+____ = 0
Answer:
1/2 -2
Step-by-step explanation:
The solution of 2x² + x − 4 = 0 is x = ( -1 ± √33 ) / 2.
What is a Quadratic Equation?A quadratic equation is what can be written in the form of ax²+bx+c=0
The equation is,
2x² + x − 4 = 0
To solve the equation, the equation needs to be factorized.
It can be also solved using the formula for determining roots.
x = ( -b ± √ (b² -4ac)) / 2a
Comparing it with the standard equation ax²+bx+c=0.
a = 2, b = 1, c = -4
Substituting the values
x = ( -1 ± √ (1² -4*2*-4)) / 2 * 2
x = ( -1 ± √ (1 + 32)) / 2 * 2
x = ( -1 ± √33 ) / 2
The solution of the given quadratic equation is x = ( -1 ± √33 ) / 2.
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find the range of the data set: 28, 11, 25, 4, 24
Suppose $1,000 is compounded quarterly for 4 years. what rate is needed to reach a total of $1,500? round to the nearest tenth of a percent.
What is the solution of the following system? -3x-2y=-12 9x+6y=-9
Answer:
No solution.
Step-by-step explanation:
Use elimination.
Multiply the equation by the opposite equation's x coefficient.
9(-3x - 2y = -12) = -27x - 18y = -108
Again, multiply by the other x coefficient.
-3(9x + 6y = -9) = -27x - 18y = 27
Add the second equation to the first.
-27x - 18y = -108
+27x + 18y = -27 The x and y will cancel each other out.
0 ≠ 135. Since 0 does not equal 135, there is no solution.
Elimination gives an equation that is always false. The two equations in the system represent parallel lines. This is an inconsistent system. It has no solutions.
Suppose you choose a marble from a bag containing 3 red marbles, 3 white marbles, and 5 blue marbles. You return the first marble to the bag and then choose again. Find P(red then blue).
The probability of first picks the red and then blue will be,15/121.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
No of red marbles =3
No of white marbles = 3
No of blue marbles =5
Total no of the marble is;
T= 3+3+5=11
The probability of picking a red ;
[tex]\rm P_{red}=\frac{3}{11}[/tex]
The probability that the next pick will be blue is;
[tex]P_{( blue})=\frac{5}{11}[/tex]
P(red then blue) is;
[tex]P_{(red \rightarrow blue})=\frac{3}{11} \times \frac{5}{11} \\\\ P_{(red \rightarrow blue})=\frac{15}{121}[/tex]
Hence,the probability of first picks the red and then blue will be,15/121.
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Solve the system of linear equations in two variables by elimination or substitution.
3x+y=7
-2x-y=9
Answer:
x=16, y=-41
Step-by-step explanation:
The volume of a sphere is a function of its radius, V=4/3(pie)(r^3). Evaluate the function for the volume of a volleyball with radius 11.4cm
Given:
Volleyball (sphere) volume[tex]=\bold{\frac{4}{3} \pi r^2}[/tex]
[tex]\to \bold{r=11.44\ cm}[/tex]
putting the value into the formula:
[tex]=\bold{\frac{4}{3} \times 3.14 \times 11.4^2}\\\\=\bold{\frac{4}{3} \times 3.14 \times 1481.544}\\\\=\bold{\frac{4}{3} \times 4652.04816}\\\\=\bold{4 \times 1550.68272}\\\\=\bold{6202.73}\\\\[/tex]
The final volume of volleyball (sphere) "[tex]\bold{6202.73\ cm^3}[/tex]".
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To find the volume of a volleyball with a radius of 11.4 cm, we plug the radius into the formula for the volume of a sphere, V=4/3(pi)(r^3), resulting in an approximate volume of 6185.7 cubic centimeters.
Explanation:The question asks to evaluate the volume of a sphere using the given formula, which is V=4/3(pi)(r^3), where V represents the volume and r is the radius of the sphere. To find the volume of a volleyball with a radius of 11.4 cm, we substitute r with 11.4 in the formula and calculate the volume accordingly.
The calculation would be:
V = 4/3 × pi × (11.4 cm)^3
V = 4/3 × 3.14159 × 11.4 cm × 11.4 cm × 11.4 cm
V = 4/3 × 3.14159 × 1481.784 cm^3
V ≈ 4/3 × 3.14159 × 1481.784 cm^3
V ≈ 6185.7 cm^3
Therefore, the volume of the volleyball is approximately 6185.7 cubic centimeters.
Round 12502 to nearest thousand
What larger conclusion can you reach by stringing together the sentences given below?If the restaurant is closed, we will eat at home.If we eat at home, we will save money.If we save money, we will become rich.
tours of the art museum are offered every 1/3 hour starting at 10 am. the museum closes at 4 pm. how many tours are offered each day
Jerome earns $200 per month plus $12 for each bike he sells at the bike shop. This month, he wants to earn at least $400. What is the least amount of bikes that Jerome can sell to reach his goal
branliest offered
which number is between -30 and 025
A. negative square root of 1610
B. negative sqare root of 680
C. negative square root of 410
D. negative square root of 27
sqrt(1610) = 40.12 = -40.2
sqrt(680) = 36.08 = -36.08
sqrt(410) = 20.25 = -20.25
sqrt(27) = 5.20 = -5.20
is that supposed to be 025 or negative 25?
the way the question is written
the answer is C & D
Let f(x) = x2 and g(x) = x − 3. Evaluate (f ∘ g)(−2).
Answer: f (g (-2)) = 25
Step-by-step explanation:
Hi, to evaluate (f ∘ g)(−2). Where:
f(x) = x2
g(x) = x − 3
As (f ∘ g)(−2) = f (g (-2))
First we find the value of g (-2) replacing the variable x by the number -2.
g (-2) =-2-3 = -5
Finally , for f(x) = x²,we replace the variable x for the value obtained (-5)
f (g (-2)) = (-5)²= 25
Feel free to ask for more if needed or if you did not understand something.
If ax-a>2a and x-1<-2
you have exactly $120 to spend on new school clothes, including 6% sales tax. What is the most that the clothes themselves can cost?
9/4x-1/2y=-3 in x and y intercepts
Answer: 4(y/2 - 3)/9
hope this helps
what is the product of −4 1/2 and 2 1/2 ?
What is the value of X? Remember to show calculations and formulas used for credit.
Two cards are randomly selected from a 52-card deck. what is the probability that the draw will yield an ace and a face card?
An ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the ___________ plane
The Cartesian plane is where an ordered pair of real numbers can be represented in a rectangular coordinate system.
In a rectangular (Cartesian) coordinate system, an ordered pair of real numbers can be represented in the Cartesian plane. The Cartesian plane is formed by the xy plane, where the x and y axes are perpendicular and intersect at the origin.
Hard math question!
What is the inverse matrix of [tex] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] [/tex]?
Please show work!
What is the value of a if (2a + 3) - 3/4 (4a - 8) = 7
Simplify the expression using properties of exponents.
12a-9b-4
9a2b6
What operation does the power 1/2 represent? Can you think of operations that other fractional powers represent, such as 1/3, 1/4 and 2/3?
Taneisha's family has signed up for a new cell phone plan. Taneisha now has a limit on the number of texts she can send or receive each month. She can text no more than 300 times per month.
1. What's is the least number of texts she can make in a month?
2.write an inequality to represent the statement. Use n for the number off texts.
3.what's is the greatest number of text she can make in a month.
4.write an inequality to represent the statement.Use n for the number of texts.
5.write the statement from parts(b) and(d) as a compound inequity.
6.write the compound inequality in compact from.
George wants to save money for a car. George invest 1300 and an account that is an interest rate of 7.5%
How many years will it take for that account 7,100?