Drag a statement or reason to each box to complete this proof.
If −3(x+8)=−21, then x=−1.
Drag a statement or reason to each box to complete this proof.
If 3x−4=14, then x=6.
Drag a statement or reason to each box to complete the proof.
If 3(x−4)=x+4, then x=8.
Answers
The different statements and reasons to prove that −3(x + 8) = −21 are as detailed below.
How to utilize properties of Algebra?Statement 1; −3(x + 8) = −21
Reason 1; Given
Statement 2; −3(x + 8)/-3 = −21/-3
Reason 2; Division property of Equality
Statement 3; x + 8 - 8 = 7 - 8
Reason 3; Subtraction Property of Equality
Statement 4; x = -1
Reason 4; Given
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Related Questions
how many centigram are equal to 9.95 milligram
Answers
Answer:
0.995 centigram
Step-by-step explanation:
divide the mass value by 10
Need help (problem and directions in the image):
Answers
Triangle ABC is congruent to triangle CDE using the side - angle - side congruence theorem. The sink hole is 52.2 ft and the Perimeter of ABC is 172.2 ft
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.
In the image shown:
AC = CE, BC = ED and they have the same angle (opposite angles are congruent).
Hence:
Triangle ABC is congruent to triangle CDE using the side - angle - side congruence theorem.
AB = DE = 52.2 ft
Perimeter of ABC = AB + BC + AC = 50 + 70 + 52.2 = 172.2 ft
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What is the center of MN given M(3, -1) and N(7,-5)
Answers
Answer:
(5, -3)
Step-by-step explanation:
So the center of the two points, or a line can be defined using the equation: [tex]midpoint=(\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})[/tex]. So using the two points you gave, you simply plug the values in to get
[tex]midpoint=(\frac{3+7}{2}, \frac{-1+(-5)}{2})\\[/tex]
Add numerators:
[tex]midpoint=(\frac{10}{2}, \frac{-6}{2})[/tex]
Simplify fraction:
[tex]midpoint=(5, -3)[/tex]
What is the simplified form of 4 log3y - 6 log3x + 7 log3z?
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[ b ] is the Correct one
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \qquad❖ \: \sf \:4 \: log_{3}(y) - 6 \: log_{3}(x) + 7 \: log_{3}(z) [/tex]
[tex] \qquad❖ \: \sf \: \: log_{3}(y {}^{4} ) - \: log_{3}(x {}^{6} ) +\: log_{3}(z {}^{7} ) [/tex]
[tex] \qquad❖ \: \sf \: \: log_{3}(y {}^{4} ) + \: log_{3}(z{}^{7} ) - \: log_{3}(x {}^{6} ) [/tex]
([tex] \sf a\: log (b) = log {b}^{a}[/tex])
[tex] \qquad❖ \: \sf \: log_{3}( {y}^{4} {z}^{7} ) - log_{3}( {x}^{6} {}^{} ) [/tex]
([tex] \sf{log (a) + log (b) = log (ab)} [/tex])
[tex] \qquad❖ \: \sf \: log_{3} \bigg( \dfrac{y {}^{4} {z}^{7} }{ {x}^{6} } \bigg ) [/tex]
([tex] \sf{log (a) - log (b) = log (a/b)} [/tex])
[tex] \qquad \large \sf {Conclusion} : [/tex]
[ b ] is the Correct choice
Find f(g(2)) if f(x) = 2x-1 g(x) = -3x Find f(g(2)) if f(x) = 2x-1 g(x) = -3x -6 -9 3 -13Let Q (in grams) represent the mass of a quantity of carbon-14, which has a half-life of 5730 years. The quantity present after t years is Q(t)=10\cdot\left(\frac12\right)^{\left(\frac t{5730}\right)}Q(t)=10⋅(
2
1
)
(
5730
t
)
.
Determine the quantity present after 2000 years.
Let Q (in grams) represent the mass of a quantity of carbon-14, which has a half-life of 5730 years. The quantity present after t years is Q(t)=10\cdot\left(\frac12\right)^{\left(\frac t{5730}\right)}Q(t)=10⋅(
2
1
)
(
5730
t
)
.
Determine the quantity present after 2000 years.
7.851 grams
1.117 grams
0.785 grams
1.745 grams
Answers
The quantity that is present after 2000 years will be A. 7.851 grams.
How to calculate the quantity?From the information given, initially at t = 0, the quantity is 10 grams.
After 2000 years, the appropriate quantity will be:
Q(2000) = 10 (1/2) × (2000/5730)
Q(2000) = 7.851 grams.
In conclusion, the correct option is A.
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Erin had 555555 stuffed bears. she took out her favorite 777 bears and then equally divided the other bears among her 333 sisters. erin's youngest sister, su, already had 151515 stuffed bears. how many stuffed bears does su have now?
Answers
The number of stuffed bears with Su=153181
What is the number of stuffed bears Su has?Total number of bears Erin has=555555
The number of bears Erin took out=777
Remaining number of bears with Erin=555555-777
=554778
Now, these remaining stuffed bears are to be divided equally among 333 sisters.
So, each sister gets [tex]\frac{554778}{333}[/tex]=[tex]1666[/tex] stuffed bears.
To find the number of stuffed bears Su has, find the sum of her share of stuffed bears and the number of stuffed bears she already had.
Number of stuffed bears Su already has=151515
Total number of bears she has at present=151515+1666
=153181
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What has to be true for the triangles to be congruent?
Answers
Answer:
Step-by-step explanation:
Argument
I think the answer is A = N or D. It that is true, then M = C because all three angles are equal which gives similarity. But there is a side involved. OM = CB. Therefore the two triangles are congruent by ASA
Answer
ASA
1. take away five from twelve times f. 2. one-half of the sum of k and six 3.x squared minus the sum of 5 4.the sum of the product of a and b, and three times c 5.twenty-four times the product of x and y, plus g.
Answers
The expressions formed are,
12f -5(k+6)/2x²-x+5ab+3c24xy+gFormation of expressions in 1, 2 and 3:
In 1, twelve times f is, 12f
Taking away 5, it becomes (12f-5)
In 2, sum of k and 6 is, (k+6)
One-half of the above quantity is, (k+6)/2
In 3, sum of 5 with x is, (x+5)
Now, x squared minus the above expression indicates (x²-x+5)
Formation of expressions in 4 and 5:
In 4, product of a and b, is ab and 3 times c is 3c
Sum of the expressions evaluated in the previous statement = ab+3c
In 5, 24 times the product of x and y is, 24xy
Adding, g in the above computed expression, we get, 24xy+g
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PLEASE HELP GUYS!!!
which of the following is equivalent to the complex number i^38?
Answers
Answer:
The answer is C = -1
Name two monomials with a quotient of 12
Answers
To babysit one child, Fernando charges $10 to drive to the appointment plus $4 per hour. He saves 30% of the total amount he earns. Brenna charges $6 per hour and saves 25% of the total amount she earns. Which equation can be used to determine the number of hours, h, after which Fernando and Brenna will have saved the same amount of money?
a 10 + 0.3(4h) = 0.25(6h)
b 0.3(10) + 4h = 0.25(6h)
c 0.3(10 + 4h) = 0.25(6h)
d 0.3(14h) = 0.25(6h)
Answers
Th equation that can be used to determine when they would have saved the same amount is 0.3(10 + 4h) = 0.25(6h).
When would they have saved the same amount?
The equation that can be used to determine the amount saved by Fernando is:
total amount saved = percentage saved x (amount charged to drive to the appointment + total amount earned)
0.3( $10 + $4h)
The equation that can be used to determine the amount saved by Brenna is:
percentage saved x total amount earned
0.25h
When they save the amount amount, the two above equations would be equal: 0.3(10 + 4h) = 0.25(6h).
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The planetary boundary layer (PBL) is the lowest layer of the troposphere; its characteristics are influenced by contact with the ground. Wind speed, temperature, and moisture in the PBL all affect weather patterns around the globe. A random sample of days was obtained and the height of the PBL (in meters) above the Great Basin Desert was measured using weather radar. Assume the underlying distribution of PBL heights is normal.
Height(m)
1 673 2 664 3 906 4 956 5 751 6 752 7 654
8 610 9 816 10 667 11 690 12 657 13 920 14 741 15 646 16 682 17 715
18 618 a. Find a 95% confidence interval for the true mean height of the PBL above the Great Basin Desert. b. Is there any evidence to suggest that the true mean height of the PBL above the Great Basin Desert is different from 700 m? There is_____to suggest that the mean height is different from 700 m. The confidence interval_____the value 700 so it is_____as the true mean height of the PBL.
Answers
The confidence interval for the true mean height of the PBL above the Great Basin Desert is (651.48,748.52) and there is any sufficient evidence that the true mean is different from 700 m .
Given Heights in meters: 673,664,906,956,751,752,654,610,816,667,690,657,920,741,646,682,715,618 and confidence level of 95%.
We have to show the evidence that the true mean height is different from 700 m.
We have to first make hypothesis.
[tex]H_{0}:[/tex]μ=700
[tex]H_{1}[/tex]:μ≠700
We have to first find the population standard deviation.
σ=[tex]\sqrt{(x-x bar)^{2}/n-1 }[/tex]
=[tex]\sqrt{187375.1/17}[/tex]
=104.98
Z=(X-μ)/σ
=(700-728.78)/104.98 (μ=728.78 is calculated in figure)
=-0.2741
p value of -0.2741 =0.39358
0.39358
0.39358<0.90
so we reject the null hypothesis.
Which means that the true mean is different from 700m.
Confidence level=X±z*s/[tex]\sqrt{n}[/tex]
Upper level=700 +1.96*104.98/[tex]\sqrt{18}[/tex]
=700+48.52
=748.52.
Lower level=700-1.96*104.98[tex]\sqrt{18}[/tex]
=700-48.52
=651.48
Hence the confidence interval is (651.48,748.52).
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
A group of high school students were surveyed about which type of movie they enjoy watching most. The results are shown in the two-way
relative frequency table below.
Female
Male
Total
Comedy
64
54
118
Drama
16
6
22
Action
20
22
42
Sci-Fi
6
27.2% 57.4% 5.7%
12
18
Use the information provided in the table to match each description with the correct percentage of students.
Total
106
94
200
18.9%
6.4%
percentage of female students who prefer sci-fi
45.8% 33.3%
percentage of students who prefer comedies that are male
percentage of male students who prefer dramas
percentage of students who prefer action movies that are female
47.6%
Answers
Answer:
a) 5.7%
b) 45.8%
c) 6.4%
d) 47.6%
Step-by-step explanation:
remember, we find percentage as:
specific / total
(ex. if we have 2 dogs and 2 cats, and we want to find what percentage of total animals are dogs, we divide 2/4 to get 0.5, or 50%)
percentage of female students who prefer sci-fi
here, we know we have 106 female students (total: 106)
and we have 6 of those students who prefer sci-fi (specific: 6)
6 / 106 = 0.05660..
which we can round to: 0.0566
So, the first percentage is 5.66%
(5.7%)
percentage of students who prefer comedies that are male
we have 118 students who prefer comedies (total: 118)
and 54 of those students that are male (specific: 54)
54 / 118 = 0.4576...
which we can round to 0.4576
So, the second percentage is 45.76%
(45.8%)
percentage of male students who prefer dramas
we have 94 male students (total: 94)
and 6 who prefer dramas (specific: 6)
6 / 94 = 0.0638298...
which we can round to 0.0638
So, the third percentage is 6.38%
(6.4%)
percentage of students who prefer action movies that are female
we have 42 students who prefer action movies (total: 42)
and 20 of those who are female (specific: 20)
20 / 42 = 0.47619..
which we can round to 0.4762
So, the fourth percentage is 47.62%
(47.6%)
hope this helps! have a lovely day :)
can someone help me ?
Answers
Answer:
∠ C = 26°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
∠ A + ∠ B + ∠ C = 180°
120° + 34° + ∠ C = 180°
154° + ∠ C = 180° ( subtract 154° from both sides )
∠ C = 26°
Solve the system of equations using elimination: -8x-4y=4 and -5x-y=-11.
Answers
The solutions to the given system of equations are x = 4 and y = -9
Simultaneous linear equationsFrom the question, we are to determine the solutions to the given system of equations
The given system of equations are
-8x-4y=4 --------- (1)
-5x-y=-11 --------- (2)
Multiply equation (2) by 4
4 ×[-5x-y=-11 ]
-20x -4y = -44 -------- (3)
Now, subtract equation (3) from equation (1)
-8x -4y = 4 --------- (1)
-(-20x -4y = -44) -------- (3)
12x = 48
x = 48/12
x = 4
Substitute the value of x into equation (2)
-5x -y = -11
-5(4) -y = -11
-20 -y = -11
-y = -11 + 20
-y = 9
∴ y = -9
Hence, the solutions to the given system of equations are x = 4 and y = -9
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Given: ΔABC with
Prove: AD/DB=CE/EB
Statement Reason
1. given
2. If two parallel lines are cut by a transversal, the corresponding angles are congruent.
3. ΔABC ~ ΔDBE AA criterion for similarity
4. Corresponding sides of similar triangles are proportional.
5. AB = AD + DB
CB = CE + EB segment addition
6. Substitution Property of Equality
7. division
8. Subtraction Property of Equality
6
What is the missing step in this proof?
A.
∠CAB ≅ ∠ACB, ∠EDB ≅ ∠DEB
B.
∠ADE ≅ ∠DBE, ∠CED ≅ ∠EBD
C.
∠CAD ≅ ∠ACE, ∠ADE ≅ ∠CED
D.
∠CAB ≅ ∠EDB, ∠ACB ≅ ∠DEB
Answers
Given that DE||AC, by similar triangles, we have;
D. <CAB congruent to <EDB, <ACB congruent to <DEBHow can the missing step be found?A part of the question that appears missing is; side DE||AC
The completed two column proof is presented as follows;
Statement. Reason
1. DE||AC 1. Given
2. <EDB congruent to <CAB
<DEB congruent to <ACB
Which can be written as; <CAB congruent to <EDB, <ACB congruent to <DEB
2. If two parallel lines are cut by a common transversal, the corresponding angles are congruent
3. ∆ABC ~ ∆DBE 3. by AA criterion for similarity
4.
[tex] \mathbf{\frac{ AB }{ CB} } = \frac{ DB }{ EB} [/tex]
4. Corresponding sides of similar triangles are proportional
5. AB = AD + DB
CB = CE + EB 5. Segment addition postulate
6. [tex] \mathbf{\frac{ AD + DB }{ CE + EB} } = \frac{ DB }{ EB} [/tex]
6. Substitution property of equality
7. [tex] \frac{ AD + DB }{ DB} = \frac{ CE + EB }{ EB} [/tex]
7. Division property
8. [tex] \frac{ AD }{ DB} + 1 = \frac{ CE }{ EB} + 1 [/tex]
[tex] \frac{ AD }{ DB} = \frac{ CE }{ EB} [/tex]
8. Subtraction property
Therefore, the missing step in the proof is the option;
D. <CAB congruent to <EDB, <ACB congruent to <DEBLearn more about similar triangles here;
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two fifth grade classes raised money for their local animal shelters. there are 20 students in class a each student raised 12 there are 26 students in class b each student in class b rasied 1.5 times as much as each student in class a
Answers
The amount the first charity got is $10.
The amount the second charity got is $20.
How much did each charity get?The first step is to determine the amount raised by the second fifth grade class: 1.5 x $12 = $18
The total amount raised by the two classes : $18 + $12 = 30
Let x represent the amount gotten by the first charity
Amount gotten by the second charity : 2x
2x + x = $30
3x = $30
x = $30 / 3
x = $10
Amount gotten by the second charity : 2(10) = $20
Two fifth grade classes raised money for their local animal shelters. there are 20 students in class a each student raised $12. there are 26 students in class b each student in class b raised 1.5 times as much as each student in class a. The money raised went to two charity. One charity received two times as much as the other. How much money did each charity receive? Show your work and explain your answer.
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Write the decimal as a fraction.
0.12
Answers
Answer:
3/25
Step-by-step explanation:
0.12=12/100
12/100 can be simplified 6/50 = 3/25
A budweiser delivery truck in west texas has driven 1,386 miles in 4 days. he leaves the distributor and stops at 24 stores during this period. between stops the driver averages ___ miles. do not count the driving back to the distributor.
Answers
Using proportions, it is found that between stops the driver averages 57.75 miles.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In 1,386 miles, the driver had 24 stops, hence the number of miles per stop is found as follows:
1386/24 = 57.75 miles.
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helppppppppppppppppppppppppppppppppppppp
Answers
2x = 10
☆...hope this helps...☆
_♡_mashi_♡_
Answer:
A. 2x = -10
E. 2x = 10
Explanation:
[tex]\sf |2x| = 10[/tex]
If |a| = b then a = b or a = -b
[tex]\sf 2x = 10 \quad or \quad 2x = -10[/tex]
divide both sides by 2
[tex]\sf x = 5 \quad or \quad x = -5[/tex]
In a function why berries directly with X in the constant of variation is two which table could represent the function
Answers
The correct option is (D)
What is a function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
the complete question is attached below
As, per the data given we can say that
the variation of quantity is 2.
So, the equation can be
y=2x
This equation defined by part (4) of the question.
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Find the sum of the geometric sequence. (7 points) 1 divided by 3, 2 divided by 3, 4 divided by 3, 8 divided by 3, 16 divided by 3
Answers
The sum of the geometric sequence is 31/3
How to determine the sum?The sequence is given as:
1/3, 2/3, 4/3, 8/3, 16/3
The sum of the sequence is;
Sum = 1/3+ 2/3+ 4/3+ 8/3+ 16/3
Evaluate
Sum = 31/3
Hence, the sum of the geometric sequence is 31/3
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Which graph represents viable values for y = 2x, where x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of the rice?
On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5).
On a coordinate plane, blue diamonds appear at points (0, 0), (1, 2), (2, 4).
On a coordinate plane, a straight line with a positive slope begins at point (negative 2.5, negative 5), crosses the x- and y-axis at point (0, 0), and ends at point (2.5, 5).
On a coordinate plane, blue diamonds appear at points (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4).
Mark this and return Save and Exit Next
Answers
The correct match for the graph of the total cost function is the option B graph.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
y = 2x is function
so, our graph should be of function y = 2x
Here, x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of the rice.
it means x is a number like 0, 1, 2, 3
so, the graph of the total cost function is a discrete function in nature.
Hence, graph-B is correct answer.
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What is the multiplicative rate of change of the function?
0.2
0.25
0.5
0.75
Answers
The multiplicative rate of change of the function will be 0.5. Then the correct option is C.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
The missing table is attached below.
For x = 2, y will be 0.125
0.125 = ab² ...1
For x = 3, y will be 0.0625
0.0625 = ab³ ...2
Divide equation 2 by equation 1, we have
b = 0.0625 / 0.125
b = 0.5
Then the correct option is C.
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Determine the vertex of the quadratic relation y=2(x+2)(x-6).
Answers
Answer:
V = (2,-32)
Step-by-step explanation:
Hello!
The vertex of a quadratic lies on the Axis of Symmetry (AOS). The axis of symmetry is exactly in the middle of the roots of the Quadratic. We can solve for the AOS by finding the average of the two roots.
Rootsy = 2(x + 2)(x - 6)0 = 2(x + 2)(x - 6)0 = (x + 2)(x - 6)0 = x + 2: x = -20 = x - 6: x = 6The two roots of the quadratic are 6 and -2.
Solve for the AOS[tex]AOS = \frac{r_1 + r_2}{2}[/tex][tex]AOS = \frac{6-2}{2}[/tex][tex]AOS = \frac42[/tex][tex]AOS = 2[/tex]The Axis of symmetry of the quadratic is 2.
VertexSince the vertex lies on the AOS, we know the x-value of the vertex. We can solve for the y-value by plugging in the value of the AOS in the equation.
Find the Vertex
y = 2(x + 2)(x - 6)y = 2(2 + 2)(2 - 6)y = 2(4)(-4)y = 2(-16)y = -32The Vertex of the quadratic is at (2,-32).
12. Todd graphs a quadratic function. The graph of his quadratic
function passes through the points
(-2,0), (4,0), and (0,-32). Which quadratic function could be Todd's
function?
a. y = 4x² - 8x - 32
b. y = 4x² + 8x - 32
C. y = 2x² - 16x - 32
d. y = -4x² + 8x - 32
a
b
OC
d
Answers
You already know that the y-intercept in -32 for every equation by plugging in 0 for x, so disregard the coordinate (0,-32). Plug in -2 and 4 as your x values and check if they are equal to your y-value 0.
y = 2x² - 16x - 32 is the quadratic function of function passes through the points (-2,0), (4,0), and (0,-32).
What is Quadratic function?y=ax²+bx+c is called as Quadratic function
y=ax²+bx+c
The three points are (-2,0), (4,0), and (0,-32)
Let,
(-2,0) in equation
0=a(-2)²+b(-2)+c
0=-2b+c...(1)
(4,0)
0=a(4)²+b(4)+c
0=16a+4b+c..(2)
(0,-32)
-32=a(0)²+b(0)+c
c=-32...(3)
Hence put c value in (1)
0=-2b-32
2b=-32
b=-16
Now put b and c value in 2
0=16(a)+4(-16)+32
0=16a-64+32
0=16a-32
a=2
Hence y = 2x² - 16x - 32 is the quadratic function of function passes through the points (-2,0), (4,0), and (0,-32).
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PLEASE 100 POINTS AND BRAINLIEST
Answers
Answer:
29u
Step-by-step explanation:
a = (V-U)/t = (1.2u-u)/10 = 0.02u
D1: V₀t+0.5at² = (u)(10)+(0.5)(0.02u)+(10)(10) = 11u
D2: (V)(t) = (1.2u)(15) = 18u
D = D1 + D2 = 29u
For first half
Initial velocity=uFinal velocity=v=1.2uTime=10sWe need acceleration first
a=(1.2u-u)/10a=0.2u/10a=0.02uSo distance traveled (Apply second equation of kinematics
s=10u+1/2(0.02u)(10)²s=10u+2/2×100/100×us=11u mFor second half
No acceleration
Distance=Speed×Time
1.2u(15)18u mTotal distance
D=11u+18uD=29u m3. Find the point of intersection of the graphs for each system. a) x - y = 1 and 3x - y = -1
Answers
Answer:
the point of intersection is (-1 , -2)
Step-by-step explanation:
[tex]\begin{cases}x-y=1&(1)\\ 3x-y=-1&(2)\end{cases}[/tex]
(2) - (1) ⇒ (3x - y) - (x - y) = (-1) - 1
⇒ 3x - y - x + y = -2
⇒ 3x - x = -2
⇒ 2x = -2
⇒ x = -1
……………………………
Now ,we can determine the value of y
by substituting x by its value -1 in the first equation (1) :
(1) x - y = 1 ⇒-1 - y = 1 ⇒ -y = 2 ⇒ y = -2
========================
Conclusion:
x = -1
y = -2
Then ,the point of intersection of the graphs is (-1 , -2)
Hello !
[tex]\begin{cases} x - y &=1 \\ 3x-y &= - 1 \end{cases} \\\Leftrightarrow \begin{cases} x =y + 1 \\ 3x-y = - 1 \: \: \: \: \: (a)\end{cases} [/tex]
We replace x by y+1 in (a) :
[tex]3(y + 1) - y = - 1 \\ 3y + 3 - y = - 1 \\ 2y = - 4 \\ y = \frac{ - 4}{2} = - 2[/tex]
Now we replace x by -1 in the first equation.
[tex]x + 2 = 1 \\ x = -1[/tex]
The point of intersection is (-1;-2).
Have a nice day
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