A set X is said to contain a set Y if every element in Y is an element in X.
[tex]X\supseteq Y\text{ or X}\subseteq Y[/tex]In this case
[tex]1\in B,\text{ 3 }\in B,5\in B,\text{ and 7}\in B[/tex][tex]\in\text{ means: is in}[/tex][tex]so\text{ m}\in N,\text{ means that m is in N}[/tex]Therefore,
[tex]B\supseteq A\text{ or A}\subseteq B[/tex]Which ordered pair is a solution to the equation? y=7x-3 O only (14) O neither only (-1,-) both (1, 4) and (-1,-4)
The givenn equation can be written as
[tex]\begin{gathered} 7x-y=3 \\ On\text{ substituting (1,4) in the left hand side of the equation we get:-} \\ 7-4=3 \\ \text{which is equal to RHS} \end{gathered}[/tex][tex]\begin{gathered} \text{Now substitute (-1,-4) in LHS of the equation} \\ -7+4=-3 \\ \text{which is not equal to RHS.} \end{gathered}[/tex]Hence only (1,4) satisfies the given equation.
So the correct option is the first one (1,4).
14.select the correct answerwhat is the sum of [tex]9.72 \times {10}^{8 \: and} 1.93 \times {10}^{7} [/tex]Answer options[tex]9.913 \times {10}^{7} [/tex][tex]9.913 \times 10 {}^{8} [/tex][tex]1.165 \times {10}^{8} [/tex][tex]1.165 \times {10}^{9} [/tex]
9.72 x 10⁸ + 1.93 x 10⁷
= 972 000000 + 193 00000
=991 300 000
= 9.913 x 10⁸
please when I send u this math explain it for me I'm only 12 and stuff is kinda hard to comprehend
First, we have to get rid of the parenthesis, to do that, we just multiply signs to get
[tex]-14-42[/tex]Now, we sum these numbers since they have the same signs
[tex]-14-42=-56[/tex]Therefore, the answer to (a) is -56.
The second operation is [tex]34+(-24)[/tex]We get rid of the parenthesis
[tex]34-24[/tex]Then, we subtract these numbers since they have different signs
[tex]34-24=10[/tex]Therefore, the answer to (b) is 10.
The third operation is[tex]-7+10[/tex]We just subtract these numbers since they have different signs
[tex]-7+10=3[/tex]Therefore, the answer to (c) is 3.
The fourth operation is[tex]-50+45[/tex]We just subtract
[tex]-50+45=-5[/tex]Therefore, the answer to (d) is -5.
The last operation is[tex]8+88[/tex]We just sum
[tex]8+88=96[/tex]Therefore, the answer to (e) is 96.
x+y=22x+7y=9can u help me solve this equation
Keeping Od, this is the solution:
x + y = 2
2x + 7y = 9
___________
Step 1: Let's isolate x in equation 1, as follows:
x + y = 2
x = 2 - y
__________________
Step 2: Let's substitute x and solve for y in equation 2, this way:
2x + 7y = 9
2 (2 - y) + 7y = 9
4 - 2y + 7y = 9
4 + 5y = 9
Subtracting 4 at both sides:
4 + 5y - 4 = 9 - 4
5y = 5
Dividing by 5 at both sides:
5y/5 = 5/5
y = 1
_______________________
Step 3: Let's substitute y and solve for x in the first equation, as follows:
x + y = 2
x + 1 = 2
Subtracting 1 at both sides:
x + 1 - 1 = 2 - 1
x = 1
_____________________
Step 4: Let's write the solution as an ordered pair, this way:
(1, 1)
Use the quadratic formula to solve the problems. Then state whether the roots are real number roots or complex number roots.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
Solving the quadratic equation using the quadratic formula, we have that:
From the solution above, we can see that the roots are complex.
[tex]\begin{gathered} \text{The roots of the equation are:} \\ x\text{ = }\frac{-5}{4}\text{ + i }\frac{\sqrt[]{31}}{4}, \\ x\text{ =}\frac{-5}{4}-i\frac{\sqrt[]{31}}{4} \end{gathered}[/tex]
(1) Which of the following statements are true? Select all that apply.
A. The data suggest that a linear model would be appropriate.
B. The data increase by a fixed amount each year.
Relative Change
XXXXX
C. The data suggest that an exponential model would be appropriate.
D. The data show a constant growth rate.
E. No model can be inferred from the data provided.
Show that the points (3, 6), (0, -2), (-7, -5) and (-4, 3) are thevertices of a parallelogram.
Let
A(3,6) B(0,-2) C(-7,-5) D(-4,3)
Remember that
A parallelogram has opposite sides congruent and parallel
so
step 1
Find out the length of the side AB
using the formula to calculate the distance between two points
[tex]\begin{gathered} AB=\sqrt{(-2-6)^2+(0-3)^2} \\ AB=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side AB
[tex]m_{AB}=\frac{-2-6}{0-3}=\frac{8}{3}[/tex]step 2
Find out the length of the side BC
[tex]\begin{gathered} BC=\sqrt{(-5+2)^2+(-7-0)} \\ BC=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side BC
[tex]m_{BC}=\frac{-5+2}{-7-0}=\frac{3}{7}[/tex]step 3
Find out the length of the side CD
[tex]\begin{gathered} CD=\sqrt{(3+5)^2+(-4+7)^2} \\ CD=\sqrt{73} \end{gathered}[/tex]Find out the slope of the side CD
[tex]m_{CD}=\frac{3+5}{-4+7}=\frac{8}{3}[/tex]step 4
Find out the length of the side AD
[tex]\begin{gathered} AD=\sqrt{(3-6)^2+(-4-3)^2} \\ AD=\sqrt{58} \end{gathered}[/tex]Find out the slope of the side AD
[tex]m_{AD}=\frac{3-6}{-4-3}=\frac{3}{7}[/tex]step 5
Compare the length of the sides
we have that
AB=CD
BC=AD
that means ----> opposite sides are congruent
Compare their slopes
mAB=mCD
mBC=mAD
that means ----> opposite sides are parallel
therefore
The given figure is a parallelogram&A(n)is formed when two rays have a common endpoint.Oline segmentangle
When two rays are with a common endpoint, an angle is formed and the common endpoint is called the vertex of the angle
Question 6 of 10
Assume that two chords in a given circle are the same distance from the
center of the circle. Which of the following must also be true?
O
A. They must be perpendicular.
B. They must be parallel.
C. They must be diameters.
D. They must be congruent.
SUBMIT
The true statement is the same distance from the center of the circle is they must be perpendicular.
We have given that,
Two chords in a given circle are the same distance from the center of the circle.
What prerequisites must be met for the chords to be in harmony?The two chords must be equally spaced apart from the circle's center if they are congruent.
A is disregarded because it's possible that the chord won't travel through the circle's center.
Because the chords are not required to be parallel, B is rejected.
Because the chords do not have to be perpendicular, C is rejected.
A chord is any line segment that joins two points on the circle's circumference. While a circle's radius connects the center to the circle's point. As a result, we can conclude that radius is not a chord based on the definitions of both terms.
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Which of the following are solutions to the inequality below? Select all that apply.
Step-by-step explanation:
1.12+8×10<66
12+80<66
92<66
2.12+8×3<66
12+24<66
36<66
3.12+8×8<66
12+64<66
76<66
4.12+8×4<66
12+32<66
44<66
therfore the answer is 2 and 4
In mid-2019, Coca-Cola Company had a share price of $39. Its dividend was $1.00 per year, and you expect Coca-Cola to raise this dividend by approximately 7% per year in perpetuity. If Coca-Cola’s equity cost of capital is 8%, what share price would you expect based on your estimate of the dividend growth rate?
The share price I would expect based on the estimate of the dividend growth rate is $10.70.
What is the share price?In order to determine the share price, the constant growth dividend model would be used. According to the model, the share price is a function of the cost of equity, dividend paid and growth rate.
Share price = next dividend / (cost of equity - growth rate)
Next dividend = current dividend x (1 + growth rate)
$1 x (1 + 0.07)
$1 x 1.07 = $1.07
Share price = $1,07 / (0.08 - 0.07)
$1.07 / 0.01 = $10.70
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Trini bought some jeans that she had been saving up for. She purchased them for $88 but has wornthem 4 times already. So far, what is the cost of wear for the jeans?
In order to find the cost of wear for the jeans, we just need to divide the cost of the jeans by the number of times Trini worn it.
So we have:
[tex]\frac{88}{4}=22[/tex]Therefore the cost of wear so far is $22.
I have tried multiple times but still could not get the correct answer or at least accurate answers
Given:
R is the midpoint of QS.
[tex]RS=5\text{,RT}=13[/tex]The midpoint is the point on a line segment equally distant from the two endpoints.
It gives,
[tex]\begin{gathered} QR=RS\ldots\ldots\text{. R is midpoint of QS} \\ \Rightarrow QR=5 \end{gathered}[/tex]Also,
[tex]\begin{gathered} RS+ST=RT \\ 5+ST=13 \\ ST=13-5 \\ ST=8 \end{gathered}[/tex]So, QT is calculated as,
[tex]\begin{gathered} QT=QR+RE+ST \\ QT=5+5+8=18 \end{gathered}[/tex]Answer: QT = 18
What is the slope of the line below? If necessary, enter your answer as afraction in lowest terms, using the slash (/) as the fraction bar. Do not enteryour answer as a decimal number or an equation.
To find the slope of a line use two points (x,y) in the next formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In the given line you have the points: (-4, -9) and (-2, -3)
[tex]m=\frac{-3-(-9)}{-2-(-4)}=\frac{-3+9}{-2+4}=\frac{6}{2}=3[/tex]Then, the slope of the given line is 3Miguel Valdez sells appliances. He is paid an 8% commission on the first $5,000 worth of sales, 10% on the next $5,500, and 15% on all sales over $10,500. What is his commission on $14,910 worth of sales?
Total Sales = 14910
8% on 5000
10% on 5500
15% on
14910 - 10500 = 4410
So,
15% on 4410 [this is the excess of 10,500]
Converting percentages to decimal:
8% = 8/100 = 0.08
10% = 10/100 = 0.1
15% = 15/100 = 0.15
Total Commission
[tex]0.08(5000)+0.1(5500)+0.15(4410)=1611.5[/tex]$1611.501) find the value of AC
2) find the measure of
1) The value of AC = 116
2) The measure of ∠BEF = 53°
What is Bisector?
When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector. Segment bisectors and angle bisectors are the sorts of bisectors that are most frequently taken into consideration.
Given,
BD is a perpendicular bisector
A is an angle bisector
BD is a perpendicular bisector then AD = DC
2n + 18 = 4n - 22
4n - 2n = 18 + 22
2n = 40
n = 40/2
n = 20
AD = 2(20) + 18
= 40 + 18
AD = 58
Now,
1) Length of AC
AC = 2AD
Here, AD = 58
AC = 2(58)
AC = 116
Hence, The value of AC is 116
2) A is an angle bisector
∠BAE = ∠DAE = 37°
∠DAE = 37°
Δ ADE is a right angle triangle
∠DEA = 90 - ∠DAE
= 90 - 37
= 53°
Since, ∠DEA = ∠BEF
∠BEF = 53°
Hence, The measure of ∠BEF = 53°
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Write this algebraic expression into a verbal expression: 1/3 ( h - 1 )
Answer:
One-third of the difference of h and 1
Simplify this equation −(4x−4)+4x−4
The equation -(4x - 4) + 4x - 4 is simplified as: -8.
How to Simplify an Equation?An equation can be simplified using the necessary properties of equalities where possible to give an expression that is simplified compared to the original equation.
Given the equation, -(4x - 4) + 4x - 4, to simplify, start by applying the distributive property of equality to open the parentheses:
-(4x - 4) + 4x - 4 = -(4x) -(+4) + 4x - 4 [distribution property of equality]
-(4x - 4) + 4x - 4 = -4x - 4 + 4x - 4
Combine like terms
-(4x - 4) + 4x - 4 = -4x + 4x - 4 - 4
Simplify the equation
-(4x - 4) + 4x - 4 = 0 - 8
= -8
Therefore, -(4x - 4) + 4x - 4 = -8.
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A glassblower makes vases. To prevent them from breaking,each vase's thickness should be 6 millimeters and candeviate by no more than 1 millimeter.Write an inequality to represent this situation, where t is thethickness in millimeters, and solve for the maximumthickness.
Since each vase should be 6 millimeters and can only deviate by no more than 1 millimeter, the inequality for the thickness would be:
[tex]6\ge t\leq7[/tex]And the maximum thickness would be 7 millimeters.
Suppose the graph of
y
=
f
(
x
)
is stretched vertically by a factor of
3
, reflected across the
x
-axis, then translated left
7
units, and up
2
units.
The new graph will have equation y=
Answer:
[tex]y=-3(x+7)+2[/tex]
Step-by-step explanation:
Alright, so the first mistake people make is to try to visualize this graph. For the sake of the problem, it does not matter in the slightest.
To start, we have y=f(x).
The first change is a vertical stretch. These are represented outside the parentheses. Meaning, the new stretched equation would be y=3(x). The three does not replace the "f", just no one would write the f into the equation as it is implied.
Next, the graph is reflected across the x-axis. This means that there is a negative outside of the parentheses. The new equation would be -3(x). As stretches are always greater than 1 and shrinks are between 0 and 1, it is clear the negative denotes a reflection.
Translations to the left are denoted as positives inside parentheses. In this case, left 7 would be -3(x+7).
Finally, upwards translations are positive numbers shown following the parentheses. Up two would make your final equation -3(x+7)+2.
42. If a pipe can drain a tank in t hours, what part of the tank does foes it drain in 3 hours? A. 3t B. t/3C. t + 3D. 3/t
Let us assume that the volume of a full tank is 1
If the tank can drain the full tank in t hours, it means that
1 = t
Let x represent the volume of the tank that would be drained in 3 hours. It means that
x = 3
We would solve both equations for x
1 = t
x = 3
By crossmultiplying,
xt = 3
x = 3/t
Thus, the correct option is D
whats the simplest term of 9m-2(3m-1)
Answer:
[tex]3m+2[/tex]
Step-by-step explanation:
I'm assuming you mean: [tex]9m-2(3m-1)[/tex] and not: [tex](9m-2)(3m-1)[/tex]
So you simply need to know the Distributive Property, which allows you to expand out values being multiplied within parenthesis without adding the values first as such: [tex]A(B+C)=AB+AC[/tex]
Applying this to distribute the -2, we get: [tex]9m-6m+2[/tex]
Adding like terms we get: [tex]3m+2[/tex]
the vertices of ABC and the endpoints of DE have coordinates that are integers. Determine the coordinates of point F so That ABC≈DEFOPTIONS:(-7, 1)(-5, 3)(-7, -8)(-2, -8)
We want figure EDF≈ABC.
We can see that if we rotate figure ABC we will obtain the following:
If we rotate it we can see that the segment AB is exactly as the segment ED.
We can now find the answer if we look how far is the point C, we see it is three unities up from B and 5 unities to its left. Then F must be 3 unities up from E and 5 unities to its left.
Since E is located :
at y = -2 if we go up 3 unities
-2 + 3 = 1
at x = -2 if we go at its left 5 unities then
-2 - 5 = -7
Then, F must be at x = -7 and y = 1.
Answer: (-7, 1)follow the order of operations and evaluate the exponential expression (5+1)^2-(9-5)^2x3
Special right trianglesFind the exact values of the side lengths c and a
Since it is a right triangle, we can use the trigonometric ratio cos(θ) to find the length c.
[tex]\cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}}[/tex]So, we have:
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \cos(45°)=\frac{c}{7} \\ \text{ Multiply by 7 from both sides} \\ \cos(45\degree)\cdot7=\frac{c}{7}\cdot7 \\ 7\cos(45\degree)=c \\ \frac{7\sqrt{2}}{2}=c \end{gathered}[/tex]Second triangleSince it is a right triangle, we can use the trigonometric ratio cos(θ) to find the length a.
So, we have:
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \cos(60°)=\frac{a}{2} \\ \text{ Multiply by 2 from both sides} \\ \cos(60°)\cdot2=\frac{a}{2}\cdot2 \\ 2\cos(60\degree)=a \\ 2\cdot\frac{1}{2}=a \\ 1=a \end{gathered}[/tex]Answer[tex]\begin{gathered} c=\frac{7\sqrt{2}}{2} \\ a=1 \end{gathered}[/tex]p(x) = x + 4; Find p(2) evaluate function
Given:
The function is,
[tex]p(x)=x+4[/tex]Explanation:
Substitute 2 for x in the function to determine the value of p(2).
[tex]\begin{gathered} p(2)=2+4 \\ =6 \end{gathered}[/tex]So answer is p(2) = 6
Given that 1 inch = 2.54 centimeters how many centimeters are in 6 feet?
Answer:
182.88 centimeters are in 6 feet!
Step-by-step explanation:
I hope this helped! c:
Answer:
182.88 centimetersStep-by-step explanation:
If
1 in. = 2.54 cm.
and
12 in. = 1 ft.
lets convert cm into feet
1 * 12 = 12 (how many inches are in a foot )
2.54 * 12 = 30.48 (how many centimeters are in a foot)
so now that we know how many centimeters are in a foot, we can find out how many centimeters are in 6 feet
30.48 * 6 = 182.88
182.88 centimeters are in 6 feetwhat is 2^-3 as a fraction
Answer:
Solution below.
Step-by-step explanation:
The question tests on the concept of indices.
We know the following indices rule:
[tex] {x}^{ - y} \\ = \frac{1}{ {x}^{y} } [/tex]
Which means by inversing the power, we will multiply the power by -1.
So in the case of this question, we can:
[tex] {2}^{ - 3} = \frac{1}{ {2}^{3} } \\ = \frac{1}{8} [/tex]
If a = (3.2) and b=(-5. 3), what is a +b?
Given the value of a and b
[tex]\begin{gathered} a=3.2 \\ b=-5.3 \end{gathered}[/tex]To get a+b
[tex]a+b=3.2-5.3[/tex]Thus
[tex]a+b=-2.1[/tex]Thus, a + b = -2.1
it takes a rat 65 seconds to run from its food source to its home. If the rat has to run 28 meters which is going faster: the rat, or a child on a bike moving at 2 m/s?
Given data:
The given distance covered by rat is d= 28 m.
The given time is t= 65 seconds.
The speed of the child is s'=2 m/s.
The expression for the speed is,
[tex]\begin{gathered} s=\frac{28}{65}\text{ m/s} \\ =0.43\text{ m/s} \end{gathered}[/tex]As the speed of the child is greater than speed of the rat, so child is going faste.
r