EXPLANATION
The value of the number in the hundreths place is 0.07
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)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).
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 3x+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)
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
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
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.
I'll send you the pic a
Let's complete the four equations, as follows:
1. 5 * x = 15
Solving for x:
5x = 15
Dividing by 5 at both sides:
5x/5 = 15/5
x = 3
3 is the value to fill in the box
2. 4 * x = 32
Solving for x:
4x = 32
Dividing by 4 at both sides:
4x/4 = 32/4
x = 8
8 is the value to fill in the box
3. 6 * x = 9
Solving for x:
6x = 9
Dividing by 6 at both sides:
6x/6 = 9/6
x = 1.5
1.5 is the value to fill in the box
4. 12 * x = 3
Solving for x:
12x = 3
Dividing by 12 at both sides:
12x/12 = 3/12
x = 3/12
Simplifying:
x = 1/4
1/4 or 0.25 is the value to fill in the box
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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Sharel spent the day at the mall. First, she bought five phones for $35each. Later, she found two five dollar bills. Write the total change to
if Sharel bought 5 phenes for 35 each, se spent 5 times 35 = $175
And when she found two $5 bills, it is like she received 2 times 5 = $10
Normally, expenses are negative numbers and earning are positive numbers, in this case
-$175 + $10 = - $165
Sothe answer is -165
Find the areas of the figure. Area of Parallelogram, Trapezoid and Composite figure. Round to the nearest hundredth where necessary.
Let
A₁ be the area of the parallelogram
A₂ be the area of the trapezoid
Solving for the area of the parallelogram
Given the following dimensions
b = 23 cm
h = 14 cm
The area is solved using
[tex]\begin{gathered} A_1=bh \\ A_1=(23\text{ cm})(14\text{ cm}) \\ A_1=322\text{ cm}^2 \end{gathered}[/tex]The area of the parallelogram therefore is 322 square centimeters.
Solving for the area of the trapezoid.
Given the following dimensions
b₁ = 15 cm
b₂ = 34 cm
h = 19 cm
The area is solved using
[tex]\begin{gathered} A_2=\frac{b_1+b_2}{2}\cdot h \\ A_2=\frac{15\text{ cm}+34\text{ cm}}{2}(19\text{ cm}) \\ A_2=\frac{49\text{ cm}}{2}(19\text{ cm\rparen} \\ A_2=(24.5\text{ cm})(19\text{ cm}) \\ A_2=465.5\text{ cm}^2 \end{gathered}[/tex]The area of the trapezoid is 465.5 square centimeters.
Solving for the area of the composite figure.
Get the sum of the two areas to get the area of the composite figure, we have
[tex]\begin{gathered} A_{\text{total}}=A_1+A_2 \\ A_{\text{total}}=322\text{ cm}^2+465.5\text{ cm}^2 \\ A_{\text{total}}=787.5\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the composite figure is 787.5 square centimeters.
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.
follow the order of operations and evaluate the exponential expression (5+1)^2-(9-5)^2x3
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 parallelogramTiffany deposited two checks into her bank account this month.One check was for $50, and the second check was for $22.Her balance at the end of the month was $306, and she made no withdrawals.Which expression shows Tiffany's balance at the beginning of the month?
Tiffany's balance at the beginning of the month = $229
Explanations:First Deposit = $50
Second Deposit = $22
End of the month balance = $306
Balance at the beginning of the month = End of the month balance - (First Deposit + Second deposit)
Balance at the beginning of the month = 306 - (50 + 22)
Balance at the beginning of the month = 306 - 77
Balance at the beginning of the month = $229
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]
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
what 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]
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.
Help please I’ll give 10 points
Choose the right symbol for the following
What are Symbols?
Many operations in mathematics are carried out using mathematical symbols. Mathematical quantities are easy to refer to thanks to the symbols. It's interesting to consider how entirely dependent mathematics is on numbers and symbols. In addition to referring to various amounts, math symbols also show how two quantities relate to one another. The primary purpose of all mathematical symbols is to carry out mathematical operations under distinct conceptions.
1) 0.02 > 0.002
2) 0.05 < 0.5
3) 0.74 < 0.84
4) 0.74 > 0.084
5) 1.2 < 1.25
6) 5.130 = 5.13
7) 3.201 > 3.099
8) 0.159 < 1.590
9) 8.269 > 8.268
10) 4.60 > 4.060
11) 302.026 > 300.226
12) 0.237 > 0.223
13) 3.033 < 3.303
14) 9.074 < 9.47
15) 6.129 < 6.19
16) 567.45 > 564.75
17) 78.967 > 78.957
18) 5.346 < 5.4
19) 12.112 < 12.121
20) 26.2 = 26.200
21) 100.32 > 100.232
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What is the mean for the data shown in the dot plot?
We will determine the mean as follows:
[tex]x=\frac{1(4)+4(5)+3(6)+2(7)+1(10)}{11}\Rightarrow x=6[/tex]So, the mean will be 6.
&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
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]Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 3x4 − 6x3 − 8x + 16(x − 2)=
Find out the division
3x^4-6x^3-8x+16 : (x-2)
3x^3-8
-3x^4+6x^3
-----------------------
-8x+16
8x-16
------------
0
The remainder is zero
that means
The expression (x-2) is a factor of the polynomial
so
3x^4-6x^3-8x+16=(x-2)(3x^3-8)
If a number with two places to the right of the decimal place is added to a number with three places to the right of thedecimal place then the answer should be reported as having how many numbers to the right of the decimal place
Let the number with two places to the right of the decimal place be represented as 20.45 and the number with three places to the right of the decimal place be 20.456
Required:
When we add the two numbers, how many numbers to the right of the decimal place is it going to have?
We can know this by adding the two fictitious numbers:
[tex]20.45\text{ + 20.456 = 40.906}[/tex]Here we can see that
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
In the circle below, if arc AB is congruent to arc CD, chord AB = 3x - 6 and chord CD = x + 12, find x.
Solution
We will equate the two values
[tex]\begin{gathered} 3x-6=x+12 \\ \\ 3x-x=12+6 \\ \\ 2x=18 \\ \\ x=9 \end{gathered}[/tex]The answer is
.. Find the values indicated. For g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)} g(-3) = g(-9) = g(-7)=
Given:
g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}
So,
To find g(-3), we need to find the term that contains -3 in the location of x of the order pair
So, g(-3) = 3
And by the same manner, we will find the others
So,
g(-9) = 12
g(-7) = 9
Last month, Ebony had 110 dollars in achecking account. The current balance is146 dollars. What is the percent change inthe account balance from last month to thismonth? Round your answer to the nearest whole percent.
Problem
Last month, Ebony had 110 dollars in a
checking account. The current balance is
146 dollars. What is the percent change in
the account balance from last month to this
month? Round your answer to the nearest whole percent.
Solutiion
For this case we can use the following formula:
[tex]\text{Change}=\frac{\text{Actual}-\text{Before}}{\text{Before}}\cdot100[/tex]And replacing we got:
[tex]\text{Change}=\frac{146-110}{110}\cdot100=32.72[/tex]And then the answer wounded to the nearest percent would be:
33%