Given the piecewise function shown below, select all the statements that are true.
A.f(-2)=0
B.f(-1)=2
C.f(4)=7
D.f(1)=0
the area of a circle is 78.5 square centimeters, and a subtending arc on the circle has an arc length of 6 pie. what is he measure of the angle subtended by the arc?
What value of f makes -35 - (-15) = f a true sentence?
Answer:
-20
Step-by-step explanation:
The two negatives will cancel each other out, so you will have -35 + 15 = f. If you add 15 to -35, you will have a smaller negative number since you are getting closer to 0.
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
A dance academy charges $24 per class and a one-time registration fee of $15. a student paid a total of $687 to the academy. find the number of classes the student took.
The student took 28 classes at the dance academy.
Explanation:The question is asking us to find out the number of dance classes the student took. This is a problem of linear equation where the total cost is the sum of the one-time registration fee and the total cost for the classes attended.
We are given the total amount paid, $687, and we know that $24 is charged per class plus a one-time fee of $15. We can represent this information in a linear equation [tex]687 = $15 + $24x[/tex], where x is the number of classes the student took.
Subtract the one-time fee from both sides of the equation you get $672 = $24x. Finally, solve for x by dividing by 24 you get x = 28. This means the student took 28 classes at the dance academy.
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Convert each number to scientific notation or standard notation.
1. 2,000
2. 91,007,500
3. 1.0395 x 1000000000
4. 4 x 100
5. 0.02
6. 0.000701
7. 8.9 x 100000
8. 4.41 x 100
Scientific and standard notation conversion for a variety of numbers.
Explanation:1. The number 2,000 can be written in scientific notation as 2 × 103. In standard notation, it remains as 2,000.
2. The number 91,007,500 can be written in scientific notation as 9.10075 × 107. In standard notation, it remains as 91,007,500.
3. The number 1.0395 × 109 is already in scientific notation. In standard notation, it would be 1,039,500,000.
4. The numbers 4, 100, and 5 are already in standard notation. In scientific notation, 4 can be written as 4 × 100, 100 can be written as 1 × 102, and 5 can be written as 5 × 100.
0.026 can be written in scientific notation as 2.6 × 10-2. In standard notation, it remains as 0.026.
0.0007017 can be written in scientific notation as 7.017 × 10-4. In standard notation, it remains as 0.0007017.
8.9 × 106 is already in scientific notation. In standard notation, it would be 8,900,000.
4.41 × 102 is already in scientific notation. In standard notation, it would be 441.
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Math?
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What is the reason for Statement 2 of the two-column proof?
A. Linear Pair Postulate
B. Angle Addition Postulate
C. Definition of bisect
D. Definition of angle
The reason for statement 2 of the two-column proof is : Definition of bisect ( optionC).
Since angle RPS is bisected, the two angles in which are formed will be equal. Bisecting an angles means dividing the angle into two equal part.
line PQ bisects RPS into two;
angle QPS = 61°
this means that RPQ is also 61°. Thus it is an acute angle. This is because 61° is an acute angle.
An acute angle is an angle that is less than 90°
Therefore, The reason for statement 2 of the two-column proof is : Definition of bisect
Help!!!!
I’ll mark you brainliest !!!
Denise is constructing A square in which two of its vertices are points M and N. She has already used her straightedge and compass to construct the lines and arcs shown.
What should Denise do for her next step?
A) use a straightedge to draw a horizontal line that contains point O.
B) use a straightedge to draw MO.
C) place the point of the compass on point M and draw any arc above it.
D) place the point of the compass on point N and draw an arc that intersects N O, using MN as the width for the opening of the compass.
Denise is constructing A square.
Note: A square has all sides equal.
We already given two vertices M and N of the square.
And another edge of the square is made by from N.
Because a square has all sides of equal length, the side NO should also be equal to MN side of the square.
Therefore, Denise need to place the point of the compass on point N and draw an arc that intersects N O, using MN as the width for the opening of the compass. That would make the NO equals MN.
Therefore, correct option is :
D) place the point of the compass on point N and draw an arc that intersects N O, using MN as the width for the opening of the compass.
Ruth borrowed $2000, part from each of two different sources, for a 6-month period. One charged 6% interest and the other 8% interest. When she paid them off, she paid a combined total of $68 in interest. How much did she borrow at each rate? Show how you got it
Write The Equation Of The Line.
Pls help I’m getting really frustrated with this question
an x intercept is where the blue line meets both the x and y coordinates given
in this graph the only one of the 4 answers that the blue line meets is (-1,0)
Solve x ym = y x3 for m.
Two trains leave stations 216 miles apart at the same time and travel toward each other. one train travels at 85 miles per hour while the other travels at 95 miles per hour. how long will it take for the two trains to meet
Final answer:
The two trains traveling towards each other at 85 mph and 95 mph respectively, will meet after 1.2 hours, as they have a combined approach rate of 180 mph.
Explanation:
To find out how long it will take for two trains to meet when they start 216 miles apart, moving toward each other at speeds of 85 miles per hour and 95 miles per hour, respectively, we can add their speeds to determine their approach rate. The sum of their speeds is the relative speed at which they are moving towards each other. Therefore, we calculate:
85 mph + 95 mph = 180 mph.
This means that the two trains cover 180 miles of the distance between them in one hour. To find the total time until they meet, we divided the total distance by their approach rate.
216 miles ÷ 180 mph = 1.2 hours.
Therefore, it will take 1.2 hours for the two trains to meet.
The sum of 5 consecutive integers is 265. What is the fifth number in this sequence?
To find the fifth number in a sequence of 5 consecutive integers with a sum of 265, you can use the formula for the sum of an arithmetic series. The fifth number is 53.
Explanation:To find the fifth number in a sequence of 5 consecutive integers where the sum is 265, we can use the formula for the sum of an arithmetic series. The formula is: Sum = (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. In this case, we have n = 5, so:
265 = (5/2)(2a + 4d)265 = 2.5a + 10da + 4d = 53Since we are looking for the fifth term, we can use the formula a + (n-1)d = 53 to solve for the fifth number:
a + 4d = 53a + 4(a+d) = 532a + 4d = 532a + 8d = 1062a + 8d - 2a - 4d = 106 - 534d = 53d = 13.25Substituting the value of d back into the equation a + 4d = 53, we can find the value of a:
a + 4(13.25) = 53a + 53 = 53a = 53 - 53a = 0Therefore, the fifth number in the sequence is a + 4d = 0 + 4(13.25) = 53.
11
The domain of the function given below is the set of all real numbers greater than 1 F(x) =(1/2)^x A. True B false
it is false for APEX
Answer:
The given statement is False.
Step-by-step explanation:
We have been given the function [tex]f(x)=(\frac{1}{2})^x[/tex] and the domain of this function is all real numbers greater than 1.
We know that the domain is the set of x values for which the function is defined.
We can see that for any real values of x, the function is defined. Therefore, the domain of the given function is the set of all real numbers.
Therefore, the given statement is False.
50 POINTS
What statement correctly describes the key features of the graph of f(x) = 4(one half)x + 1 − 3?
A. Y-intercept of (0, −1), starts up on the left, gets closer to y = −3 on the right
B. Y-intercept of (0, −1), starts down on the left, gets closer to y = −3 on the right
C. Y-intercept of (0, 1), starts up on the left, gets closer to y = −3 on the right
D. Y-intercept of (0, 1), starts down on the left, gets closer to y = −3 on the right
Answer:
Option D correctly describes the key features of the graph of the function.
Explanation:
To analyze the given function [tex]\( f(x) = 4(0.5x) + 1 - 3 \)[/tex], let's break it down:
1. The function is in the form [tex]\( f(x) = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
2. The coefficient of [tex]\( x \), \( 0.5 \)[/tex], represents the slope of the line. Since it's positive, the line is increasing from left to right.
3. The y-intercept occurs when [tex]\( x = 0 \)[/tex]. Substituting [tex]\( x = 0 \)[/tex] into the function, we find [tex]\( f(0) = 4(0.5 \times 0) + 1 - 3 = 1 - 3 = -2 \).[/tex] So, the y-intercept is (0, -2).
Now, let's consider the options:
A. Y-intercept of (0, −1), starts up on the left, gets closer to y = −3 on the right - Incorrect.
B. Y-intercept of (0, −1), starts down on the left, gets closer to y = −3 on the right - Incorrect.
C. Y-intercept of (0, 1), starts up on the left, gets closer to y = −3 on the right - Incorrect.
D. Y-intercept of (0, 1), starts down on the left, gets closer to y = −3 on the right - Correct.
Use the information given to enter an equation in standard form. Slope is -6, and (7, 5) is on the line.
To find the standard form of a line with a given slope and a point, use the point-slope formula, plug in the values, and rearrange into Ax + By = C.
To enter an equation in standard form using the given information that the slope is -6 and the point (7, 5) is on the line, we start by using the point-slope formula:
y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope. Plugging in the values, we have:
y - 5 = -6(x - 7)
Now we distribute the slope on the right side:
y - 5 = -6x + 42
Adding 5 to both sides to solve for y gives us:
y = -6x + 47
To get the standard form, Ax + By = C, we add 6x to both sides:
6x + y = 47
This is the equation in standard form
12=-4(-6x-3)+2x work it out for me and tell me how many solutions
Heather is a cashier. She can ring up 12 customers in 9 minutes. At this rate, how many minutes does it take her to ring up 4 customers?
9 minutes / 12 customers = 0.75 minutes per customer
4 customers x 0.75 minutes per customer = 3 minutes total for 4 customers
Boats can travel anywhere between 50 and 150 kilometers per hour. Choose a speed between 50 and 150. Convert the speed you chose into meters per second
/: You work out. /: You practice your free throws in basketball. /: You are a starting player. Write the following compound statement in symbolic form. If you work out and practice your free throws in basketball, then you will be a starting player.
Final answer:
To convert the compound statement into symbolic form using propositional logic, we assign P to 'You work out', Q to 'You practice your free throws', and R to 'You are a starting player', resulted in the symbolic representation \((P \land Q) \rightarrow R\).
Explanation:
To write the compound statement 'If you work out and practice your free throws in basketball, then you will be a starting player.' in symbolic form, you can use propositional logic symbols. Let's define the simple statements first:
P: You work out.
Q: You practice your free throws in basketball.
R: You are a starting player.
The compound statement combines these simple statements using the logical connective 'and', symbolized by \(\land\), and the implication 'then', symbolized by \(\rightarrow\). The symbolic form of the compound statement is:
\((P \land Q) \rightarrow R\)
This reads as 'If P and Q are true, then R will also be true.'
Number 35 Plz someone help me in this problem ❤️
Please help. I'm horrible at equations
Solve for x. 2x/3+1=3
x = 1 1/3
x = 2 2/3
x = 3
x = 6
If a cookie recipie cals for 4, 1/4 cups if flour and you cut the ricipie in half ,how much flour would you nuse
divide 4 1 /4 cups by 2
4/2 = 2
1/4 / 2 = 1/8
so 2 1/8 cups are needed
Find the value of 3 + 4(16 - 9)
Dont forget to use order of operations btw
31
49
58
List the intercepts, vertex, and axis of symmetry for each quadratic function whose graph is shown.
331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?
Write an equation for the line parallel to y= -7x+15 that contains p(9,-6)
The equation of a line parallel to y = -7x + 15 that passes through the point (9,-6) is y = -7x + 57.
Explanation:The question asks for an equation of a line parallel to y = -7x + 15 that passes through the point p(9,-6). Parallel lines have the same slope. Thus, the slope of our new line is also -7. In the form y = mx + b, 'm' represents the slope and 'b' is the y-intercept. We know the slope and a point on the line, but we don't know the y-intercept. We can plug the point p' s coordinates (9,-6) into the equation and solve for 'b'.
Therefore, -6 = -7(9) + b results in b = 57. So, the equation of the requested line is y = -7x + 57.
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Consider the parabola: y=−2x2−16x−27. what is the linear equation for the axis of symmetry for this parabola?
The linear equation for the axis of symmetry for the parabola y = -2x² - 16x - 27 is x = -4.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.
Consider the parabola: y=−2x²−16x−27.
The axis of symmetry of a parabola is a line that divides the parabola into two mirror images.
For a parabola in the form y = ax² + b x + c, the axis of symmetry is a vertical line that passes through the vertex of the parabola.
The x-coordinate of the vertex is given by -b/(2a), so the equation of the axis of symmetry for the given parabola is :
x = -(-16)/(2×-2) = -4.
Therefore, the required axis of symmetry for the parabola is x = -4.
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