Answer:
[tex]x=8[/tex]
Step-by-step explanation:
We have been given that [tex]AC=3x+6[/tex] and [tex]CD=2x+14[/tex].
To solve for x, we are assuming that C is the midpoint of segment AD and we will equate both expressions as:
[tex]3x+6=2x+14[/tex]
[tex]3x-2x+6=2x-2x+14[/tex]
[tex]x+6=14[/tex]
[tex]x+6-6=14-6[/tex]
[tex]x=8[/tex]
Therefore, the value of x is 8.
PLEASE ANSWER ASAP!!! WORTH 13 POINTS! I need help D:
Lucy's goal for her cycling class at the gym is to burn 450 calories in one hour. The number of calories (c) she actually burns in one hour varies no more than 45 calories. Which inequality below represents this scenario?
A) |c − 450| less than or equal to 45
B) |c + 450| greater than or equal to 45
C) |c − 45| less than or equal to 450
D) |c − 45| greater than or equal to 450
Guys help me out with this one plizz
Getting two 6's in four rolls can happen in 6 ways. 4C2 = 6
The probability of getting two 6's is 1/36. Therefore,
6 times 1/36 = 1/6 or 0.16666666...
Converting to a percent to the nearest tenth is 16.7%
I really need help :(...............
Jess observed that 60% of the people at a mall on a particular day shopped for clothes. If 2500 people at the mall did not shop for clothes that day, the number of people who shopped for clothes that day was ______.
Answer:
3750
Step-by-step explanation:
3750
Parallel to the line 2x-3y=9 and having a y intercept of 3
Help with these three problems? Please
6. add the averages then take that average
50+74 = 124, 124/2 = 62
answer: 62
8. first put all the numbers in order
4, 5 ,6 ,8 11, 12,14, 15, 23 ,23
Find the middle number, since there are 10 numbers find the average of the 2 middle numbers
11+12 =23/2 =11.5
Lower half data = 4, 5, 6, 8, 11
The middle number of that set is Q1,
Q1=6
9
9, find q3
1, 2, 3, 5, 5, 6, 9
Find middle number (5)
upper half data = 5, 6, 9
Q3= 5 , 6, 9 = 5+10 +15 = 30
so answer is $30
Stan and hilda can mow the lawn in 30 min if they work together. if hilda works twice as fast as stan, how long does it take stan to mow the lawn alone?
There are (72)3 ⋅ 70 lambs on a farm. What is the total number of lambs on the farm?
Heyyy guys just thought I’d let y’all know the answer is *117649* if you (7^2)^3 that’s the answer and 7^0 is 0 soooo yeah!
How many 3 digit numbers can be made if no digit is repeated and the number can not begin with a zero?
digit #1 - 9 numbers (1-9)
digit #2 = 9 numbers (0-9 minus the first digit)
digit #3 = 8 numbers ( 0-9 minus the first 2 digits)
9*9*8 = 648 combinations
What is the measure of an exterior angle of a regular 11-sided polygon?
The measure of an exterior angle of a regular 11-sided polygon is 32.73°.
The measure of an exterior angle of a regular 11-sided polygon can be calculated using the formula:
60° divided by the number of sides.
In this case, for an 11-sided polygon, each exterior angle would measure 360° / 11 = 32.73°.
Which equation is not equivalent to the formula m = ca?
A: [tex]c = \frac{m}{a} [/tex]
B: [tex]a = \frac{c}{m} [/tex]
C: [tex]a = \frac{m}{c} [/tex]
D: m = ac
Answer:m=ca i remember my teacher telling me how to do this.
Step-by-step explanation:
3. Simplify log3 20 - log3 5
Which of the following is a key property of the linear parent function
A it is in quadratic ll and lV
B is has a slope of 1
C it is a curved line
D it does not go through the origin
Answer:
The correct option is B.
Step-by-step explanation:
The equation of linear parent function is
[tex]y=x[/tex]
Key property of the linear parent function are:
1. It is in quadratic l and lII.
2. It has a slope of 1.
3. It is a straight line.
4. It passes through the origin.
The graph of parent function is shown below.
In the given options only the statement " It has a slope of 1" is true.
Therefore the correct option is B.
If θ is in Quadrant III and cosθ -2/3, then sinθ = _____.
Answer:
[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
Step-by-step explanation:
If θ is in Quadrant III
[tex]\cos\theta=-\dfrac{2}{3}[/tex]
As we know in III quadrant cosine and sine both are negative.
using trigonometry identity
[tex]\sin\theta=-\sqrt{1-\cos^2\theta}[/tex]
[tex]\sin\theta=-\sqrt{1-(\frac{2}{3})^2}[/tex]
[tex]\sin\theta=-\sqrt{1-\frac{4}{9}}[/tex]
[tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
Hence, The value of [tex]\sin\theta=-\dfrac{\sqrt{5}}{3}[/tex]
In the diagram below, what is the approximate length of the minor arc ?
arc length = given angle/360 x 2 x PI x radius
120/450 x 2 x 3.14 x 23 = 48.17
round to 48 cm
Answer:
Option A is correct
the approximate length of the minor arc is, 48 cm
Step-by-step explanation:
Length of an arc is given by:
[tex]l = r \theta[/tex] .....[1]
here r is the radius of the circle from the center and [tex]\theta[/tex] is the angle in radian.
From the given figure, we have;
r = 23 cm
Use conversion:
1 degree = 0.0174533 radian
then
120 degree = 2.094396
[tex]\theta = 2.094396[/tex] radian.
Substitute these in [1] we have;
[tex]l = 23 \cdot 2.094396 = 48.171108[/tex] cm
Therefore, the approximate length of the minor arc is, 48 cm
Find the exact values of sin A and cos A. Write fractions in lowest terms. A right triangle ABC is shown. Leg AC has length 15, leg BC has length 20, and hypotenuse AB has length 25.
In the right triangle with sides 15, 20, and 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.
In the right triangle ABC, we can use the given side lengths to find the trigonometric ratios for angle A. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the legs (AC and BC).
Let's denote the angle A as angle A:
Find sin A:
sin A = (opposite / hypotenuse) = BC / AB = 20 / 25 = 4/5.
Find cos A:
cos A = (adjacent / hypotenuse) = AC / AB = 15 / 25 = 3/5.
So, the exact values are sin A = 4/5 and cos A = 3/5.
In summary, in the right triangle ABC with side lengths AC = 15, BC = 20, and AB = 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.
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If four times a number plus 3 is 11, what is the number
Three out of four students in a school said they would vote for nuncio for class president. Predict how many of the 340 students would vote for nuncio
The velocity of a train, measured in meters per second, is described by vector t=(-1,-4). Find the direction the train is traveling using standard position
Answer:
inverse tangent 4/1
75.96 + 180 bc 3rd quadrant which equals 255.96 degrees.
Step-by-step explanation:
round 256 degrees
The end points of AB are A(-2,-3) , B(3,2) point C lies on AB and is 2/5 of the way from A to . What is the coordinates of point C? Explain how you find your answer
To find the coordinates of point C which divides line AB into a 2:5 ratio, use the section formula. Therefore, the coordinates are (-4/7, -11/7). This provides point C's location on the line segment AB.
Explanation:The coordinates of C are determined through the section formula, which finds the coordinates of a point dividing a line segment into a specific ratio. In this case, the ratio is 2:5. To solve for the x-coordinate of C, the formula [(m*x2) + (n*x1)] / (m+n) is used, where m and n are the ratio values, x1 and x2 are the x-coordinates of points A(-2, -3) and B(3, 2). Using these, the x-coordinate of C is found to be (2*3 + 5*(-2)) / (2+5) = -4/7.
Similar calculations apply to solving for the y-coordinate of C: [(m*y2) + (n*y1)] / (m+n) = (2*2 + 5*(-3)) / (2+5) = -11/7.
Therefore, the coordinates of point C are (-4/7, -11/7). This is the point C on the line segment AB that is 2/5 of the way from point A to point B.
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Quadrilateral $abcd$ is a trapezoid with $ab$ parallel to $cd$. we know $ab = 20$ and $cd = 12$. what is the ratio of the area of triangle $acb$ to the area of the trapezoid $abcd$? express your answer as a common fraction.
Determine the common ratio and find the next three terms of the geometric sequence.
3/4,3/10,3/25,...
The next three terms of the sequence are 6/125, 12/625 and 24/3125
Geometric sequenceThe nth term of a geometric sequence is given as:
Tn = ar^n-1
Given the geometric sequence
3/4,3/10,3/25,...
Find the common ratio
r = 3/10 * 4/3
r = 2/5
Find the 4th, 5th and 6th terms
T4 = (3/4)(2/5)^3
T4 = 3/4 * 8/125
T4 = 6/125
T5 = (3/4)(2/5)^4
T5 = 3/4 * 16/625
T5 = 12/625
T6 = (3/4)(2/5)^5
T6 = 3/4 * 32/3125
T6 = 24/3125
Hence the next three terms of the sequence are 6/125, 12/625 and 24/3125
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A caterer expects a minimum of 160 but no more than 192 people at a wedding. One fruit tray serves 16 people. The compound inequality represents x, the number of fruit trays the caterer should bring to the wedding.
160 ≤ 16x≤ 192
Which is a possible number of fruit trays the caterer might bring to the wedding?
A. 8
B. 10
C. 14
D. 16
Answer:
b. 10
Step-by-step explanation:
I did the test
A worker produced a total of 198 mousetraps during a 6 hour run with no rejects and no downtime. A report states that this worker produced at a rate of 2 mousetraps per minute. Based on the actual production, is the rate of 2 mousetraps per minute accurate?Exit Test
Based on the actual production, the rate of 2 mousetraps per minute is not accurate.
What is Rate?Rate of a quantity is the amount of that quantity with respect to some amount of another quantity.
If the quantity with respect to which the rate is measured is taken as single unit or one unit, then the rate is called unit rate.
Production of mousetraps by the worker in 6 hours = 198
Production of mousetraps by the worker in 1 hour = 198/6 = 33
That is, production of mousetraps by the worker in 60 minutes = 33
Production of mousetraps by the worker in 1 minute = 33/60 = 0.55
The worker produced mousetraps at a rate of 0.55 mousetraps per minute.
But the report states that this worker produced at a rate of 2 mousetraps per minute, which is not correct.
Hence the statement of report that the worker produced at a rate of 2 mousetraps per minute is not accurate, because he is only producing 0.55 mousetraps per minute.
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Write the equation in standard form for the parabola with vertex (0,0) and directrix y=-6
To find the equation of a parabola with a vertex at (0,0) and a directrix of y=-6, we determine the focus is at (0,6), leading to the standard form equation of the parabola as y = 1/4x^2.
Explanation:The question asks for the equation of a parabola in standard form given its vertex at (0,0) and directrix as y=-6. In parabolic equations, the standard form is usually y = ax^2 + bx + c for horizontal parabolas, or x = ay^2 + by + c for vertical parabolas. Given the vertex is at the origin (0,0) and the directrix is y = -6, this means the focus is at (0,6) because the distance from the vertex to the focus is equal to the distance from the vertex to the directrix but in the opposite direction.
For a parabola that opens upwards or downwards, the standard form is y = ax^2 (since the vertex is at the origin, b and c are 0). Given that the distance from the vertex to the focus (which is also the distance from the vertex to the directrix) is 6, the parabola opens upwards, and its focal distance (p) is 6. Hence, the value of 4p = 24, which leads us to conclude that a = 1/4. Therefore, the equation of the parabola is y = 1/4x^2.
8y - 1 = x 3x = 2y Solve the system of equations by substitution.
.........simplify 3^2*3^5
How to tell if there is a horizontal asymptote?
To tell if there is a horizontal asymptote, for rational functions, compare the degrees of the numerator and denominator; if they are equal, the asymptote is the ratio of their leading coefficients. If the numerator's degree is less, the asymptote is at y=0; if greater, there is no horizontal asymptote. Polynomials do not have horizontal asymptotes.
To determine if a function has a horizontal asymptote, we look at the behavior of the function as x approaches infinity (x →∞). For rational functions, the degrees of the numerator and denominator play a crucial role. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. For instance, as x approaches infinity, the term with the highest power dominates and the constant terms become less significant, leading to the horizontal asymptote at y = 1.
In a scenario where the degree of the numerator is less than the degree of the denominator, the function will have a horizontal asymptote at y = 0, since the function approaches zero as x increases without bound. Conversely, if the degree of the numerator is greater than the degree of the denominator, no horizontal asymptote exists because the function grows without limit.
Remember, polynomials do not have horizontal asymptotes, as their values continue to increase or decrease indefinitely with x.
The measure of an inscribed angle is 110°. What is the measure of the intercepted arc? 55° 110° 220°
the measurement of an inscribed angle is half of the measure of the intercepted arc.
the inscribed angle is 110 degrees, so we multiply 110 by 2.
110*2 = 220 degrees
The measure of the intercepted arc is 220 degrees
220° is the measure of the intercepted arc
Solve the quadratic equation by completing the square.
x^2-10x+15=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
^ Please use the template above to answer ^
To solve the quadratic equation x^2 - 10x + 15 = 0 by completing the square, we manipulate it to the form (x - 5)^2 = 10, then solve for x to get two solutions: x = 8.16 and x = 1.84.
Explanation:To solve the quadratic equation by completing the square, we need to manipulate the equation x^2 - 10x + 15 = 0 so it takes the form of (x - a)^2 = b, where a is half of the coefficient of x, and b is a constant.
First, we move the constant to the other side of the equation:
x^2 - 10x = -15
Next, we find the value that completes the square. This value is (10/2)^2 = 25.
Adding 25 to both sides, we get:
x^2 - 10x + 25 = 25 - 15
Now the equation is a perfect square:
(x - 5)^2 = 10
To find the solution for x, we take the square root of both sides:
x - 5 = ±10√10
x = 5 ± √10
Thus, the solutions rounded to the nearest hundredth are:
x = 5 + √10 ≈ 8.16
x = 5 - √10 ≈ 1.84
The complete answer in the template is:
Form:
( x - 5 )^2 = 10
Solution:
x = 8.16, 1.84