[tex] \frac{ - 1}{3} (6x + 15) - 3 \\ \\ 1. \: \frac{ - 6x + 15}{3} - 3 \\ 2. \: \frac{ - 3(2x + 5)}{3} - 3 \\ 3. \: - (2x + 5) - 3 \\ 4. \: - 2x - 5 - 3 \\ 5. \: - 2x + ( - 5 - 3) \\ 6. \: - 2x - 8[/tex]
Final answer:
To simplify -1/3 (6X +15) -3, distribute the -1/3 across the parentheses to get -2X - 5, and then subtract 3 to get the equivalent expression: -2X - 8.
Explanation:
The student's question is asking for the equivalent expression of -1/3 (6X +15) -3. To find the equivalent expression, we start by distributing the -1/3 across the parentheses:
-1/3 × 6X = -2X
-1/3 × 15 = -5
Next, we combine this result with the -3 that is outside of the parentheses:
-2X - 5 - 3 = -2X - 8
Therefore, the equivalent expression is -2X - 8.
Which is the correct answer a,b,c, or d. Need to now ASAP!
Answer:
I think C
Step-by-step explanation:
Graph x^2 +y^2=9. What are the lines of symmetry
Answer:
The lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.
Step-by-step explanation:
Without graphing, this is the equation of a circle with center at the origin,
(0, 0) and with a radius of 3 units. The general equation of a circle with center (a, b) and with radius r units is given as;
[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]
The graph of the function is as shown in the attachment below;
A line of symmetry cuts the graph of a function into two equal parts such that these parts become mirror images of each other.
For the case of a circle, the line that divides the circle into two equal portions is the diameter. Any given circle has infinite number of diameters.
Therefore, the lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.
The vertices of a triangle are A(−6, −3), B(0, 3), and C(−6, 0). Draw its image after a dilation with respect to the origin using a scale factor of 1/3. All I need to know is the points of the new triangle.
Thanks!
Answer:
A'(-2, -1), B'(0, 1), C'(-2, 0)
Step-by-step explanation:
When dilation is about the origin, the scale factor multiplies each individual coordinate.
A' = (1/3)A = (-6/3, -3/3) = (-2, -1) . . . . for example
The rest is mental arithmetic, since all given coordinate values are divisible by 3.
the radius of a circle with an area of a circle with an area of 60 square centimeters is represented by the expression sqrt 60/x centimeters. what is another way of expressing the radius?
Answer:
[tex]\dfrac{2\sqrt{15\pi}}{\pi}[/tex]
Step-by-step explanation:
[tex]\displaystyle\sqrt{\frac{60}{\pi}}=\sqrt{\frac{4\cdot 15\pi}{\pi^2}}=\frac{2}{\pi}\sqrt{15\pi}[/tex]
coefficient of x^2 in expansion of the binomial theorem (2x-1)^4 show your work
Answer:
24
Step-by-step explanation:
If you use Pascal's triangle, which I did, you will look at the 5th row of the triangle which contains the numbers 1, 4, 6, 4, 1
If we expand using a = 2x and b = -1, then the expansion looks like this:
[tex]1(2x)^4(-1)^0+4(2x)^3(-1)^1+6(2x)^2(-1)^2+4(2x)^1(-1)^3+1(2x)^0(-1)^4[/tex]
If you simplify all that down by multiplying, you'll get
[tex]16x^4-32x^3+24x^2-8x+1[/tex]
If you don't know how to use Pascal's triangle, you need to learn. It's so very cool!
The expression (3x2 + 5x – 12) – 2(x2 + 4x +9) is equivalent to which of the following:
A. x2 – 3x – 30
B. x2 + 13x + 6
C. 5x2 + x – 18
D. x2 + 3x – 21
Show Your Work
Answer:
A. x² -3x -30
Step-by-step explanation:
Using the distributive property to eliminate parentheses, we get ...
3x² +5x -12 -2x² -8x -18
Then, collecting terms gives ...
= (3-2)x² +(5-8)x +(-12-18)
= x² -3x -30 . . . . . . . . . . . . . matches selection A
I need help with both these questions please
Answer:
2. 90°
3. 65°
Step-by-step explanation:
2. Points A, B, and D are on a semicircle centered at C. The angle A is inscribed in that semicircle, so is 90°. Then angles B and D sum to 90°.
__
3. Triangle ABC is similar to triangle EDC by SAS, so angle x has the same measure as the third angle of triangle EDC: 180° -80° -35° = 65°.
___
The relevant relationship in both cases is that the sum of angles in a triangle is 180°. Also, for problem 2, you need to know that an inscribed angle has half the measure of the arc it subtends. And for problem 3, it helps to understand the relationships in similar triangles.
which fraction is closer to 1/2 than to 0 or 1
A fraction is closer to 1/2 than to 0 or 1 if its numerator is more than half of 0 and less than half of the denominator. For instance, 3/5 is closer to 1/2 than to 0 or 1 because its numerator is more than half of 0 and less than half of 5.
Explanation:To determine which fraction is closer to 1/2 than to 0 or 1, consider the numerical value of the fractions in relation to 1/2. As a rule of thumb, if a fraction has a numerator that is half the denominator, it equals 1/2. When the numerator is less than half the denominator, the value is less than 1/2; when the numerator is over half the denominator, the value is greater than 1/2.
For example, if we take 1/3, it is clear that this value is less than 1/2 because the numerator, 1, is less than half of the denominator, 3. Comparatively, the fraction 2/3 is closer to 1 than to 1/2 since the numerator, 2, is greater than half of the denominator, 3.
Another example would be comparing 3/5 and 4/5 to 1/2. The fraction 3/5 has a numerator that is more than half of the denominator, making it closer to 1/2 than to 0 or 1, while 4/5 is closer to 1. Therefore, 3/5 is the fraction that is closer to 1/2 than to 0 or 1.
A fraction closer to 1/2 than to 0 or 1 falls in the range (> 1/3 but < 2/3); 5/8 is an example of such a fraction. An intuitive understanding and the use of a common denominator can aid in identifying and comparing these fractions.
Explanation:Determining which fraction is closer to 1/2 than to 0 or 1 involves understanding the number line and how fractions fall on it.
To identify such a fraction, it should be evident that any fraction greater than 1/2 will naturally be closer to 1, while any fraction less than 1/2 is closer to 0.
Therefore, we look for a fraction in the range (> 1/3 but < 2/3) to ensure it is closer to 1/2.
By using the intuitive sense of fractions, which is like having an understanding of fractions through visualization or practical examples, we can gauge the closeness to 1/2.
For instance, we know that 1/3 is less than 1/2, and similarly, 2/3 is more than 1/2.
Following this line of reasoning, the addition of fractions (1/3 + 1/6 = 1/2) indicates that 1/6 is the gap needed to reach from 1/3 to 1/2.
A fraction such as 5/8 would be a good example of a fraction closer to 1/2.
This fraction is more than 1/2 (4/8) but less than 3/4 (6/8), placing it comfortably closer to 1/2 on the number line.
Employing the common denominator strategy also helps to compare fractions effectively, by aligning them to a unifying reference point.
Please help asap
Inverse of a Function
Answer:
[tex]f^{-1} (x)=-\frac{1}{6}x+1[/tex]
Step-by-step explanation:
To find the inverse of a function in equation form, first I recommend changing the f(x) to a y:
y = -6x + 6
Next step is to switch the x and y:
x = -6y + 6
Now solve for the new y:
x - 6 = -6y and
[tex]-\frac{1}{6}x + 1=y[/tex]
You can put the inverse notation back in for y like I did in the answer section above.
Find the perimeter and area of this figure
it is made up of semicircles and quarter circles
please use the actual symbol pi, do not simplify
Answer:
A = (16π -32) in²
P = (4π +8√2) in
Step-by-step explanation:
The area is that of a quarter-circle of radius 8 inches less half the area of a square with side length 8 inches. Two formulas are useful:
area of a circle = πr² . . . . .r = radius
area of a square = s² . . . . s = side length
Then your area is ...
A = (1/4)π(8 in)² - (1/2)(8 in)² = (64 in²)(π/4 -1/2)
A = (16π -32) in²
____
The applicable formulas for the side lengths of your figure are ...
arc BD = (1/4)(2πr) = π(r/2) = π(8 in)/2 = 4π in
segment BD = (8 in)√2
The perimeter is the sum of these lengths, so is ...
P = (4π +8√2) in
_____
Of course, you are very familiar with the fact that an isosceles right triangle with side lengths 1 has a hypotenuse of length √(1²+1²) = √2. Scaling the triangle by a factor of 8 inches means the segment AB will be 8√2 inches long.
WRITE THE EQUATION OF THE PARABOLA with a directrix of y=1 and a focus of (0,-1).
Answer:
-4y = x², or y = - x²/4, or y = -(1/4)x²
Step-by-step explanation:
Because the focus is beneath the directrix, this vertical parabola opens down. The general formula is 4py = x².
Because the distance between focus and directrix is 2 units, p = -1 here. The negative sign shows that the parabola opens down.
4py = x² becomes 4(-1)y = x², or -4y = x², or y = - x²/4
whast is the value of -3/4-(-3/8)?
Answer:
- 3/8
Step-by-step explanation:
- 3/4 - (-3/8)
= -3/4 + 3/8
= -6/8 + 3/8
= - 3/8
Yannick and Jean are playing a guessing game with integers. Yannick wrote these clues to help Jean guess the unknown integer. n+6 greater than or equal to 15 and n+5<15 What is the value of the unknown integer, n?
Answer:
9
Step-by-step explanation:
The solution to ...
n +6 ≥ 15
is found by subtracting 6:
n ≥ 9
__
The solution to ...
n +5 < 15
is found by subtracting 5:
n < 10
__
The only integer that is at least 9 and less than 10 is 9.
The value of the unknown integer, n, is 9.
Use the constant term and leading coefficient to list all the potential roots of the expression.
5x4 + x3 + 3x2 - 7
Using the information, what is the factors of constant?
Answer: 1,7 and 1,5 on coefficient
Step-by-step explanation:
Equation at the end of step 1 :
(((5•(x4))+(x3))+3x2)-7
Step 2 :
Equation at the end of step 2 :
((5x4 + x3) + 3x2) - 7
Step 3 :
Checking for a perfect cube :
3.1 5x4+x3+3x2-7 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 5x4+x3+3x2-7
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 3x2-7
Group 2: 5x4+x3
Pull out from each group separately :
Group 1: (3x2-7) • (1)
Group 2: (5x+1) • (x3)
3.3 Find roots (zeroes) of : F(x) = 5x4+x3+3x2-7
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 5 and the Trailing Constant is -7.
The factor(s) are:
of the Leading Coefficient : 1,5
of the Trailing Constant : 1 ,7
The factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].
Given
Expression; [tex]\rm 5x^4+x^3+3x^2-7[/tex]
What is the leading coefficient?The leading coefficient of the polynomial of the term has the highest degree of the polynomial.
The factors of the constant term;
[tex]\rm 5x^4+x^3+3x^2-7=0\\\\ 5x^4-4x^3+7x^2-7x+5x^3-4x^2+7x-7=0\\\\(x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex]
Hence, the factor of the constant is [tex]\rm (x+1) (5x^3-4x^2+7x-7) =0\\\\[/tex].
To know more about the Leading coefficient click the link given below.
https://brainly.com/question/13577114
Determine and prove what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value.
A(24, −8), B(12, −17), C(3, −5), D(15, 4)
The shape is a .
The perimeter of ABCD is .
The area of ABCD is .
Answer:
square; 60; 225.
Step-by-step explanation:
1) using the vectors rules to calculate the lengths of the sides AB; BC; CD and AD. When AB=BC=CD=AD it means, the shape is a square of rhombus.
2) using the vectors rules to calculate the lengths of the diagonales AC and BD. When AC=BD it means, the shape is a square.
3) The perimeter of the square ABCD is 15*4=60.
4) The area of the square ABCD is 15*15=225.
All the details are in the attached picture; answers are marked with colour.
Twenty people report for jury duty. How many different 12 perosn juries can be chosen
Answer:
125,970
Step-by-step explanation:
Even if jury are assigned numbers, the order in which they are picked has no importance. That means that it's a combination, not a permutation.
The formula to calculate possible combinations is:
[tex]C(n,r) = \frac{n!}{(r! (n-r)!)}[/tex]
Where n is the global population, and r is the number of selected items.
In our case, n = 20 and r = 12, so...
[tex]C(20,12) = \frac{20!}{(12! (20-12)!)} = 125970[/tex]
There are 125970 different ways to select 12 jury members out of 20 people.
there are 125970 different 12 person juries that can be chosen from a pool of 20 people.
The question is asking how to determine the number of different ways to choose a 12-person jury from a pool of 20 potential jurors. This type of problem is solved using the concept of combinations in mathematics, specifically the binomial coefficient formula which is given by the following:
C(n, k) = n! / (k!(n - k)!)
where:
n represents the total number of items (in this case, jurors).
k represents the number of items to choose (jurors to be selected for the jury).
n! means factorial of n, which is the product of all positive integers up to n.
In this scenario, n = 20 and k = 12. Therefore, the number of different 12 person juries that can be chosen is calculated as:
C(20, 12) = 20! / (12!(20 - 12)!)
Further calculation yields:
C(20, 12) = 20! / (12!8!) = 125970
Therefore, there are 125970 different 12 person juries that can be chosen from a pool of 20 people.
What is the surface area of the above composite object made out of two rectangular prisms?
700 mm^2
550mm^2
600mm^2
450mm^2
625mm^2
Answer:
550 mm^2
Step-by-step explanation:
A net can be drawn as shown in the first figure attached. Each square represents 5 mm by 5 mm, so is 25 mm^2. Altogether, there are 22 of them, so the total area is ...
(25 mm^2)·22 = 550 mm^2
The second attachment shows that net folded up to make the given figure.
_____
In the first attachment, the green shades represent the left- and right-side faces. (Darker green is left side.) The red and blue shades represent the front- and back-side faces. The white rectangles represent the top and bottom faces. The dark black lines are the cut lines. If you want to fold the figure up, the lighter lines are the fold lines.
The second attachment is just verification that all faces are accounted for and the net actually corresponds to the given figure.
!PLEASE HELP! WILL GIVE BRAINLIEST!!
A projectile launched straight up into the air with an initial velocity of 20 meters per second from a height of 10 meters. How long will it take for the projectile to hit the ground?
please solve and show your work!!
The key on a map shows 3/8th of an inch is 60 miles. If two cities are 4 5/8 inches apart, what is this value in miles?
Answer: 740 miles
Step-by-step explanation:
You know that [tex]\frac{3}{8}inches[/tex] on the map is actually 60 miles and the distance between these two cities is [tex]4\ \frac{5}{8}inches[/tex].
You can express this distance as a decimal number:
[tex](4+0.625)inches=4.625inches[/tex]
Therefore, let be "d" the distance in miles between these two cities.
Then, you get:
[tex]d=\frac{(4.625inches)(60miles)}{(\frac{3}{8}inches)}\\\\d=740miles[/tex]
Which figures demonstrate a single reflection?
Select each correct answer.
Answer:
Please see the attached image below, to find more information about the graph
The figures that are obtained by a single reflection are shown in the image inside a red rectangle.
The axis of reflection is shown with a black line.
- The figure from the left shows horizontal reflection
- The figure from the right shows vertical reflection
A crane lifts 50 Newtons 2 meters. How much work is done?
50 Nm
100 Nm
200 ft-lbs
2 Nm
Answer:
Step-by-step explanation:
2 meter is like 6.4 yards
so i would say B is the answer
Final answer:
The work done by the crane in lifting 50 Newtons over a distance of 2 meters is 100 Nm.
Explanation:
The work done by a crane can be calculated by multiplying the force applied by the distance over which the force is applied. In this case, the crane is lifting 50 Newtons over a distance of 2 meters. Therefore, the work done is:
Work = Force x Distance
Work = 50 N x 2 m = 100 Nm
So, the correct answer is 100 Nm.
A rectangle prism with a volume of 4 cubic units is filled with cubes with side lengths of 1/3 unit. How many 1/3 unit cubes does it take to fill the prism?
Check the picture below.
so is filled with those cubes, recall that a cube has all equal sides, in this case 1/3, so the volume of each cube is simply the product of length*width*height.
[tex]\bf \stackrel{\textit{volume of one cube}}{\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\implies \cfrac{1}{27}}\qquad \qquad \stackrel{\textit{if there are \underline{x} cubes inside then their total volume is}}{\cfrac{1}{27}x~~~~=~~~~\stackrel{\textit{volume of prism}}{4}} \\\\\\ x=27\cdot 4\implies x=108[/tex]
simply
[tex]\sqrt[4 ]{162 {b}^{8} } [/tex]
Answer:
see below
Step-by-step explanation:
[tex]\sqrt[4]{162b^8}=\sqrt[4]{2\cdot 3^4b^8}=\sqrt[4]{2(3b^2)^4}\\\\=3b^2\sqrt[4]{2}[/tex]
Kendra surveyed a random sample of 100 members of a local gym. She found that 40% of the gym members surveyed had taken a yoga class. Kendra wanted to know if it is plausible that 50% of the entire population of gym members had taken a yoga class. Kendra performed 100 trials of a simulation. Each trial simulated a sample of 100 gym members under the assumption that 50% of the population had taken a yoga class. The dot plot shows the results of the simulations. What is the best conclusion for Kendra to make based on the data?
A. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
B. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is likely.
C. It is plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
D. It is plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is likely.
Answer: A, it is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
Answer:
Option A is correct.
Step-by-step explanation:
Kendra surveyed a random sample of 100 members of a local gym. She found that 40% of the gym members surveyed had taken a yoga class.
Kendra performed 100 trials of a simulation. Each trial simulated a sample of 100 gym members under the assumption that 50% of the population had taken a yoga class.
The best conclusion based on the plot is - A. It is not plausible that 50% of the population had taken a yoga class because the data shows that a sample proportion of 40% is unlikely.
Given: m VKP =148° Find: m∠JPV
Answer:
106
Step-by-step explanation:
VPL=1/2VkP
VKP=148
VPL=74
JPV+VPL=180
JPV=106
The measurement of angle JPV from the considered situation is found as m∠JPV = 106°
What is the angle the radius makes on the point of contant of a tangent of a circle?The radius which touches the point where the tangent touches too on a specified circle, is perpendicular to the tangent (90 degrees angle with the tangent).
Referring to the image attached below, we're provided that:
m arcVKP = central angle arc VKP subtends = m∠VOP = 148°
The perpendicular from center O on the line VP (VP is a chord) bisects it, and therefore, the triangle ODP and ODV are congruent by SAS congruency [ side OD is common, the angle (the 90 degree) on either side of OD is of same measure, and VD and DP are of same measure due to OD bisecting VP).
Thus, we get:
[tex]m\angle POD = m\angle VOD[/tex]
But since we have:
m∠POD + m∠VOD = m∠VOP = 148°
thus, m∠POD + m∠POD = 148°
or m∠POD = 148°/2 = 74° = m∠VOD
Now, as sum of angles in a triangle is 180°, therefore, for triangle OPD, we get:
[tex]m\angle OPD + m\angle ODP + m\angle POD = 180^\circ\\x^\circ + 90^\circ + 74^\circ = 180^\circ\\x = 16[/tex]
Thus, we get the measurement of angle JPV as:
[tex]m\angle JPV = m\angle JPO + m\angle OPD\\ m\angle JPV = 90^\circ + x^\circ = (90 + 16)^\circ = 106^\circ[/tex]
Thus, the measurement of angle JPV from the considered situation is found as m∠JPV = 106°
Learn more about tangent here:
https://brainly.com/question/7942024
Verify the identity
Answer:
We have to prove
sin(α+β)-sin(α-β)=2 cos α sin β
We will take the left hand side to prove it equal to right hand side
So,
=sin(α+β)-sin(α-β) Eqn 1
We will use the following identities:
sin(α+β)=sin α cos β+cos α sin β
and
sin(α-β)=sin α cos β-cos α sin β
Putting the identities in eqn 1
=sin(α+β)-sin(α-β)
=[ sin α cos β+cos α sin β ]-[sin α cos β-cos α sin β ]
=sin α cos β+cos α sin β- sinα cos β+cos α sin β
sinα cosβ will be cancelled.
=cos α sin β+ cos α sin β
=2 cos α sin β
Hence,
sin(α+β)-sin(α-β)=2 cos α sin β
What is the solution to the inequality below? 12x > 6(x - 2)
Answer:
x > -2
Step-by-step explanation:
12x > 6 (x - 2)
12x > 6x - 12
6x > - 12
x > - 2
Can someone please just make some equations for me? I would be so grateful. Look at the graph.
3) For Zach, if his heart beats 15 times in 10 seconds, his heart beats 1.5 times in 1 second. Multiply this by 25 to get the number of times his heart will beat in 25 seconds → 1.5 * 25 = 27.5 times per 25 seconds. 1.5 * 60 = 90 times per minute. 1.5 * 120 = 180 times per two minutes. Do the same for your heart beats. 14 beats per 10 seconds is 1.4 beats per second. 1.4 * 25 = 35 times per 25 seconds. 1.4 * 60 = 84 times a minute. 1.4 * 120 = 168 times per two minutes.
4) Zach's equation would be H = 1.5n and yours would be H = 1.4n
5) Your heat beats just a little bit slower than Zachs. Everyone is different and there are many different things that can affect heart rate. Maybe he walked a little more than you did or maybe he was stressing about something which made his heart beat a little faster.
I hope this helps you!
jenna buys 8 packets of letter paper. Each packet contains 12 sheets of paper. She uses 16 sheets of letter paper a week. How many weeks will it take her to use all the letter paper?
She will take 6 weeks.
Answer:
She will take 6 weeks.
hope this helps
A student researcher compares the heights of men and women from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 1111 men had a mean height of 70.870.8 inches with a standard deviation of 2.432.43 inches. A random sample of 1717 women had a mean height of 66.366.3 inches with a standard deviation of 2.322.32 inches. Determine the 98%98% confidence interval for the true mean difference between the mean height of the men and the mean height of the women. Assume that the population variances are equal and that the two populations are normally distributed. Step 3 of 3 : Construct the 98%98% confidence interval. Round your answers to two decimal places.
Answer:
Answer me please??!!
Step-by-step explanation: