Answer:
Every integer greater than 1 is either prime or composite.
Step-by-step explanation:
Let us negate this statement.
Assumption - any number greater than 1, is neither prime nor composite.
A prime number has only 2 divisors, and a composite number has at least 3.
Let a number be X such that X >1.
Now X is divisible by 1 (Any integer is divisible by 1)
And X is divisible by X (X/X = 1, if X is not zero)
So by this, we see X has at least 2 divisors, X is either prime, or composite if it has more divisors!
So our assumption is wrong, and every integer greater than 1 is either prime or composite.
Select the equation that represents the graph of the line y=x-1 y=1/2x-1 y=1/2x + 2 y=x+2
Answer:
[tex]y = \frac{1}{2}x - 1[/tex]
Step-by-step explanation:
Given
See attachment for graph
Required
The graph equation
First, pick any two corresponding points on the line
[tex](x_1,y_1) = (2,0)[/tex]
[tex](x_2,y_2) = (4,1)[/tex]
Calculate slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{1 - 0}{4 - 2}[/tex]
[tex]m = \frac{1}{2}[/tex]
The line equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where
[tex](x_1,y_1) = (2,0)[/tex]
[tex]m = \frac{1}{2}[/tex]
So:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = \frac{1}{2}(x - 2) + 0[/tex]
[tex]y = \frac{1}{2}x - 1 + 0[/tex]
[tex]y = \frac{1}{2}x - 1[/tex]
HURRY! Roberto concluded that 8th graders are more likely than 9th graders to have a summer job because more 8th graders than 9th graders responded that they have a summer job. Is Roberto correct? Explain why or why not
Answer :What words or phrases did the author use to express his opinion about city gardening?
Step-by-step explanation:
A circle has a radius of 17 in. Find the length s of the arc intercepted by a central angle of 0.7 radians.
Round your answer to the nearest tenth .
Given:
The radius of the circle is 17 in.
Central angle of intercepted arc is 0.7 radians.
To find:
The length s of the intercepted arc.
Solution:
The formula for the length of intercepted arc is:
[tex]s=r\theta[/tex]
Where, r is the radius of the circle and [tex]\theta [/tex] is the central angle in radians.
Substituting [tex]r=17,\ \theta =0.7[/tex] in the above formula, we get
[tex]s=17\times 0.7[/tex]
[tex]s=11.9[/tex]
Therefore, the length of the intercepted arc is 11.9 inches.
A phone originally cost £70 and is increased to £77
What is the percentage increase?
Answer:
mark me brainliest
Step-by-step explanation:
10% increased
Answer:
10%
Step-by-step explanation:
100%-> 70
1%->0.7
77-70=7
7÷0.7=10
Which factors of −14 are used to factor x2+5x−14?
Answer:
+ 7 and - 2
Step-by-step explanation:
Given
x² + 5x - 14
Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (+ 5)
The factors are + 7 and - 2 , since
7 × - 2 = - 14 and 7 - 2 = + 5 , then
x² + 5x - 14 = (x + 7)(x - 2) ← in factored form
Find the value of x.
Find the area of a circle with a circumference
of 50.24 units.
units2
Use 3.14 for II and label your answer in square units. Ex: 4 square units OR 4 units squared
Answer:
Hello! answer: 200.96
Step-by-step explanation:
50.24 ÷ 3.14 = 16 16 ÷ 2 = 8 8 × 8 × 3.14 = 200.96 therefore are area is 200.96 HOPE THAT HELPS!
Answer:
200.96
Step-by-step explanation:
Khan academy
HELP ASAP PLEASE
(3^2)^4
Answer:
6561
Step-by-step explanation:
3^2= 3*3=9 9^4= 9*9*9*9= 6561
Answer:
[tex]((3)^2)^4 = (9)^4 = 6561\\\\\\OR\\\\\\(3)^2)^4= 3^8 = 6561[/tex]
I NEED HELP IMMEDIATELY!!!! PLS HELPP. PLS DO NOT GUESS EITHER BUT PLS CMON AND HELP ME PLSSS
Answer:
The Clubhouse and the Swimming Pool
Step-by-step explanation:
If you look closely the points are on the buildings. The X axis is left to right.
The Clubhouses coordinate is (12,12) but the Swimming Pools coordinates is (8,12). They have the same X-Axis
Answer:
club house and swimming pool
Step-by-step explanation:
club house and swimming pool both have an x-coordinate of 12.
0
100%
Which expression is equivalent to (-11x2 +1.4x-3) + (4x2-2.7x+8)
What is the slope of the line that passes through the points (2.1) and (17, -17)? Write your answer in simplest form.
how would this be done??
Answer:
the answer is
-17-1/17-2=-18/15=Slope
find the mode from the given below:
b. Age
Age &
No.of stule
10
20
28
210
22
16
Answer:
no mode
Step-by-step explanation:
because their is no reptetion on the number
pls ans.thanks a lot
Answer:
you're answer is -2
Step-by-step explanation:
i hope this helped you have a nice day :)
An art class contains 87 jars of paint. One third of the paint colors is red the remaining two thirds is purple.what is the ratio of purple paint to red paint.
9514 1404 393
Answer:
2 : 1
Step-by-step explanation:
purple : red = (2/3) : (1/3) = 2 : 1
The ratio of purple paint to red paint is 2 : 1.
Answer:
Solution :-⅓ are red
So,
No. of red colors = 1/3 × 87 = 29
No. of purple colors = 2/3 × 87 = 2 × 29 = 58
So,
Ratio = 58:29
Ratio = 2:1
[tex] \\ [/tex]
Write a polynomial expression that has the following characteristics: The polynomial expression is a trinomial. The polynomial expression has degree 2. The leading coefficient is -5. 6
Answer:
[tex] { - 5.6}xy ^{2} + yx + 2x[/tex]
Expand the following logarithm:
[tex] log_{5}( \frac{ {x}^{2} }{y} )^{6} [/tex]
Answer:
[tex] \displaystyle 12 \log_{5}( {x}^{} {)}^{} - 6 \log_{5}(y ^{} )[/tex]
Step-by-step explanation:
we would like to expand the following
[tex] \displaystyle \log_{5}\bigg( \frac{{x}^{2}}{y} \bigg) ^{6} [/tex]
since we have a division of two different variable we can consider using division logarithm rule
[tex] \displaystyle \log_{5}( {x}^{2} {)}^{6} - \log_{5}(y) ^{6} [/tex]
use law of exponent:
[tex] \displaystyle \log_{5}( {x}^{12} {)}^{} - \log_{5}(y ^{6} )[/tex]
by exponent logarithm rule we acquire:
[tex] \displaystyle 12 \log_{5}( {x}^{} {)}^{} - 6 \log_{5}(y ^{} )[/tex]
and we are done!
Arc measure - Hello! Can you please help me and if you can explain the formula that would be awesome!
9514 1404 393
Answer:
88°
Step-by-step explanation:
Angle MQP is called an "inscribed angle." Its vertex (Q) is on the circle, and its sides are chords of the circle. The ends of the sides intercept arc MP. The relationship between an inscribed angle and the intercepted arc is that the measure of the arc is twice the measure of the angle.
arc MP = 2×∠MQP = 2×44°
arc MP = 88°
Use the graph to write a linear function that relates y to x
Answer:
y=-4x
Step-by-step explanation:
Select 2 points, I will be using (-1,2) and (0,-2)
As you can see, for every x unit to the left, there are four y units down
Pablo wants to pour 82.69 grams of salt into a container. So far, he has poured 38.4 grams. How much more salt should Pablo pour?
please help =)
helppppp
Answer:
44.29 grams
Step-by-step explanation:
82.69 - 38.4 gives you 44.29.
44.29 + 38.4 gives you 82.69.
Please help I’m failing the class!! also please show your work if possible thanks!
9514 1404 393
Answer:
m∠c = 52°
Step-by-step explanation:
Corresponding angles are congruent:
13x +11° = 15x -7° . . . . . the corresponding angles have equal measures
18° = 2x . . . . . . . . . . . . add 7° -13x to both sides
9° = x . . . . . . . . . . divide by 2
Now, we can find c. It is supplementary to the corresponding angles.
c = 180° -(15x -7°) = 180° -15(9°) +7° . . . . . substitute for x
m∠c = 52°
Which group(s) reported having the widest range of time to relax? Please estimate what that range is.
Answer:
Divorced ; Never married
Step-by-step explanation:
The range of a dataset can be obtained from a boxplot by taking the difference of the readings of the minimum and maximum values. These values are culled from the boxplot by taking the reading on the endpoint of the lower whisker and endpoint of the upper whisker respectively. In the figure Given, we Can deduce that the divorced group and never married group have the widest range of time to relax
Maximum = 8
Minimum = 0
Estimated range: Maximum - Minimum = (8 - 0) = 8
7/2 x+1/2x=1/2+9/2x help
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]\frac{7}{2}x+\frac{1}{2}x=\frac{1}{2}+\frac{9}{2}x[/tex]
Step 1: Simplify both sides of the equation.
[tex]\frac{7}{2}x+\frac{1}{2}x=\frac{1}{2}+\frac{9}{2}x[/tex]
[tex](\frac{7}{2}x+\frac{1}{2}x)=\frac{9}{2}x+\frac{1}{2}[/tex] (Combine Like Terms)
[tex]4x=\frac{9}{2}x+\frac{1}{2}[/tex]
[tex]4x=\frac{9}{2}x+\frac{1}{2}[/tex]
Step 2: Subtract [tex]\frac{9}{2}x[/tex] from both sides.
[tex]4x-\frac{9}{2}x=\frac{9}{2}x+\frac{1}{2}-\frac{9}{2}x[/tex]
[tex]\frac{-1}{2}x=\frac{1}{2}[/tex]
Step 3: Multiply both sides by [tex](\frac{2}{-1})[/tex].
[tex](\frac{2}{-1})*(\frac{-1}{2}x)=(\frac{2}{-1})*(\frac{1}{2})[/tex]
[tex]x=-1[/tex]
Therefore, [tex]x=-1[/tex] will be your final answer.
Sorry this took very long. I had to calculate all of this.
DUS is a 30°-60°-90° triangle with short leg SU. If SU = x, determine the
length of the long leg and the length of the hypotenuse.
Answer:
SD = 2x
UD = x[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The hypotenuse of a 30-60-90 triangle is 2 times the length of the shorter leg.
SU is the shorter leg = x
So, SD = 2x
The longer leg of a 30-60-90 triangle is [tex]\sqrt{3}[/tex] times the shorter leg.
So, UD = x[tex]\sqrt{3}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
In a 30-60-90 triangle the sides are in the ratio 1:√3:2 so if the shortest side SU = x then the long leg = √3x and the hypotenuse = 2x.
Please write the domain, range, equation and parent function
Answer:
See below
Step-by-step explanation:
26. Domain: {x|x ≥ 2}
Range: {y| y ≤ -3}
Parent: y = [tex]\sqrt{x}[/tex]
Equation: y = [tex]\sqrt{x - 2} - 3[/tex]
27. Parent: y = | x |
Equation: y = - | x + 2 | + 3
Domain: Reals
Range: {y | y ≤ 3}
Now, I am not going to do all 6 of these problems. Hopefully the ones I did will give you an idea of what needs to be done.
I will tell you this: 28 is an exponential function
29 is a quadratic function, 30 is an exponential function and 31 is a cubing function. Good luck.
Rotate the given triangle
90°clockwise about the origin.
21
2 21
-1 3
?
1
Answer:
Step-by-step explanation:
-1 -1 3
1 -2 -2
The new coordinates of the vertices after a 90° clockwise rotation about the origin are:
[tex]\left[\begin{array}{ccc}-1&1&-3\\1&2&2\\\end{array}\right][/tex]
What occurred when you rotated 90 degrees clockwise?If we rotate a triangle 90° counter clockwise about the origin,
Then if one of its vertices be (x, y), it will be changed to (y, x).
The triangle is given as follows:
[tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\\\end{array}\right][/tex]
To rotate the given triangle 90° clockwise about the origin, we can use the rotation matrix:
[tex]\left[\begin{array}{ccc}cos90^{o}&-sin90^{o}\\sin90^{o}&cos90^{o}\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0&-1\\1&0\\\end{array}\right][/tex]
To apply this rotation matrix to each vertex of the triangle, we multiply it with the coordinate vector of each vertex.
Let's denote the vertices of the triangle as A, B, and C.
A = (-1, -1)
B = (2, -1)
C = (2, 3)
Applying the rotation matrix to each vertex, we have:
[tex]A' = \begin{bmatrix} 0 & -1 \ 1 & 0 \end{bmatrix} \begin{bmatrix} -1 \ -1 \end{bmatrix} = \begin{bmatrix} 1 \ -1 \end{bmatrix}[/tex]
[tex]B' = \begin{bmatrix} 0 & -1 \ 1 & 0 \end{bmatrix} \begin{bmatrix} 2 \ -1 \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix}[/tex]
[tex]C' = \begin{bmatrix} 0 & -1 \ 1 & 0 \end{bmatrix} \begin{bmatrix} 2 \ 3 \end{bmatrix} = \begin{bmatrix} -3 \ 2 \end{bmatrix}[/tex]
Therefore, the new coordinates of the vertices after a 90° clockwise rotation about the origin are:
A' = (1, -1)
B' = (1, 2)
C' = (-3, 2)
This can be written as follows:
[tex]\left[\begin{array}{ccc}-1&1&-3\\1&2&2\\\end{array}\right][/tex]
Learn more about the rotating triangle here:
https://brainly.com/question/22878771
#SPJ7
(2m - 5m^3 ) - (5m + 3m^3- 7m^4 ) + (8 - 3m^3- 5m^4+ 4m)
Answer:
2m^4 - 11m³ + m + 8
Step-by-step explanation:
(2m - 5m³) - (5m + 3m³ - 7m^4) + (8 - 3m³ - 5m^4 + 4m)
2m - 5m³ - 5m - 3m³ + 7m^4 + 8 - 3m³ - 5m^4 + 4m
7m^4 - 5m^4 - 5m³ - 3m³ - 3m³ + 2m - 5m + 4m + 8
2m^4 - 11m³ + m + 8
Answer:
8 + m - 11m^3 + 2m^4
Step-by-step explanation:
Add and subtract like terms:
8 + (2m - 5m +4m) + (-5m^3 - 3m^3 - 3m^3) + (7m^4 - 5m^4) =
8 + m - 11m^3 + 2m^4
The formation of the solar system
Step-by-step explanation:
Our solar system formed about 4.5 billion years ago from a dense cloud of interstellar gas and dust. The cloud collapsed, possibly due to the shockwave of a nearby exploding star, called a supernova. When this dust cloud collapsed, it formed a solar nebula—a spinning, swirling disk of material.
Answer:
Our solar system formed about 4.5 billion years ago from a dense cloud of interstellar gas and dust. The cloud collapsed, possibly due to the shockwave of a nearby exploding star, called a supernova. When this dust cloud collapsed, it formed a solar nebula—a spinning, swirling disk of material. It was gaseous, filled with billions of stars.
Mark me brainliestt :)) ehehe
find the product of (p+3q2)pq
Answer:
p²q + 3pq³
Step-by-step explanation:
(p + 3q²) pq ← multiply each term in the parenthesis by pq
= p²q + 3pq³
Find the percent of change.
A coat costs $250 and is on sale
for $100.
The percent of change in price is________
Answer:
150
Step-by-step explanation:
250 - 100
What is simplifying? I honestly know what it is, but I forgot the definition.