If the shared side between angles 1 and 2 has a measure of 2x+7 and the shared side between angles 3 and 4 has a measure of 7x+3, what is the value of X?
Round your answer to the nearest hundredth.
Answers
Answer:
x = 0.8Step-by-step explanation:
Both mentioned sides have equal length as opposite sides of a parallelogram.
Set equation and solve for x:
2x + 7 = 7x + 37x - 2x = 7 - 35x = 4x = 4/5x = 0.8Related Questions
kayla used her cell phone for four days . her average calling time was 130 minutes each day .suppose that kayla used the phone for m minutes on fifth day . write an algebraic expression for the average number of minutes she spent on the phone over five days.
Answers
Answer:
130-60m
Step-by-step explanation:
shopping at savers mart, Lisa buys her children four shirts and three pairs of pants for $85.50. she comes back the next day and buys three shirts and five pairs of pants for $115. What is the price of each shirt and each pair of pants.
Answers
=
$
7.50
price for one pair of pants
=
$
18.50
Explanation:
Start by letting variables
x
and
y
represent the pieces of clothing from the problem.
Let
x
be the price of one shirt.
Let
y
be the price of one pair of pants.
Equation
1
:
4
x
+
3
y
=
85.50
Equation
2
:
3
x
+
5
y
=
115.00
You can solve for each variable by using elimination or substitution. However, in this case, we will use use elimination. First, we will solve for
y
, the price of each pair of pants.
To isolate for
y
, we must eliminate
x
. We can do this by making the two equations have the same
x
values. First, we find the LCM of
4
and
3
, which is
12
. Next, multiply equation
1
by
3
and equation
2
by
4
so that
4
x
and
3
x
becomes
12
x
in both equations.
Equation
1
:
4
x
+
3
y
=
85.50
3
(
4
x
+
3
y
)
=
3
(
85.50
)
12
x
+
9
y
=
256.50
Equation
2
:
3
x
+
5
y
=
115.00
4
(
3
x
+
5
y
)
=
4
(
115.00
)
12
x
+
20
y
=
460.00
Now that we have two equations with
12
x
, we can subtract equation
2
from equation
1
to solve for
y
.
12
x
+
9
y
=
256.50
12
x
+
20
y
=
460.00
−
11
y
=
−
203.50
y
=
18.50
⇒
price for one pair of pants
Now that we know that a pair of pants is
$
18.50
, we can substitute this value into either equation
1
or
2
to find price for one shirt. In this case, we will choose equation
1
.
4
x
+
3
y
=
85.50
4
x
+
3
(
18.50
)
=
85.50
4
x
+
55.5
=
85.50
4
x
=
28
x
=
7.50
⇒
price for one shirt
∴
, the price for one shirt is
$
7.50
and the price for one pair of pants is
$
18.50
.
Ned help pretty please someone
Answers
The missing value is 22
Direct Proportionality:Direct proportion is the relation between two quantities or values where the ratio of the two will always equal a constant value. The symbol used for proportion is the symbol '∝'.
When two quantities are in direct proportion, if we increase one value, then the other will also increase, and if we decrease one value then the other value will also decrease.
Here we have
x - 1 2 3 4 5
y - -2 4 10 16 ?
As we see the value of x is directly proportional to y
For every 1 unit value of x, the y value is increasing 6 units
For more Understand observe the following
at x = 1 => y = -2
at x = 2 => y = -2 + 6 = 4
at x = 3 => y = -2 + 2(6) = 10
Therefore,
The relation between x and y can derive as given below
=> y = - 2 + (x-1)6
=> y = - 2 + 6x -6
=> y = 6x - 8
at x = 5 => y = 30 - 8 =22
Therefore,
The missing value is 22
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HELPP PLEASE IM ACTUALLY STUCK???
Answers
Answer:
[tex]d=-8[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]258[/tex] and the second term is [tex]250[/tex], then each successive term in the sequence is [tex]8[/tex] less than the previous term. Therefore, the common difference is [tex]-8[/tex] ( [tex]d=-8[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=-8n+266[/tex]
Therefore:
Term 1: [tex]a_1=-8(1)+266=-8+266=258[/tex]
Term 2: [tex]a_2=-8(2)+266=-16+266=250[/tex]
Term 3: [tex]a_3=-8(3)+266=-24+266=242[/tex]
…
Term 9: [tex]a_9=-8(9)+266=-72+266=194[/tex]
Which points are on the axes 5 units from the origin
Answers
Answer: X
Step-by-step explanation:
you just start at 0 since that is the origin and go up 5
Please help me with these questions
Answers
The rate of change of the linear functions given in tabular form and equations are found as follows;
1. a. The rate of change of the function is 5
b. The rate of change of the function is 7
c. The rate of then function is 0.75
d. The function has a rate of change of -8
2. The rate of change of the function of -4, indicates that each unit increase in the input value results in 4 unit decrease in the output values
b. The number of days it took for the patients blood sample to have 360 antibodies is 13 days
c. The rate of change of the function is 20, which indicates that the antibody in the patients blood is increasing at a rate of 20 antibodies each day
The rate of change of a function is a measure of how much the output changes per unit change in the input.
1. The rate of change of the functions are as follows;
a. The first difference of the y-values is constant, therefore the function is a linear function
The formula for the rate of change of the linear function is presented as follows;
[tex]m = \dfrac{y_2-y_1}{x_2 - x_1}[/tex]
The rate of change of the function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{-3 - (-8)}{1 - 0} = 5[/tex]b. The first difference is constant and equal to 7, the rate of change of the straight line function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{49-42}{1-0} = 7[/tex]
The rate of change of the function is 7 unit changes in the y-value per unit change in the x-valuesc. The function is a linear function, as the first difference is constant and equal to 0.75
The rate of change of the function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{2.25-1.5}{-4-(-5))} = 0.75[/tex]
The rate of change of the function is 0.75d. The first difference is constant and equal to -8
The rate of change of the straight line function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{5 - 13}{1 - 0} = -8[/tex]
The rate of change of the function is -82. a. The rate of change of the function, y = -4·x + 1 is found by taking the slope of the function
The function is the equation of a straight line, of the form, y = m·x + c with the slope, m = -4
The rate of change of the function is -4, such that for each unit increase in the input value, the output value decreases by 4 units
b. When the number of antibodies is 360, we have;
360 = 20·d + 100
20·d = 360 - 100 = 260
d = 260 ÷ 20 = 13
It would take 13 days for the patients blood to have 360 antibodiesc. The rate of change of the function means that the number of antibodies the drug produces in the patients body each day is 20 antibodies.
3. The function that gives the amount of antibodies in the body is a = 20·d + 100
d = The number of days
a = The number of antibodies
a. The table is completed as follows;
Data for Medicine A
d [tex]{}[/tex] a
0 [tex]{}[/tex] 100
1 [tex]{}[/tex] 120
2 [tex]{}[/tex] 140
3 [tex]{}[/tex] 160
4 [tex]{}[/tex] 180
5 [tex]{}[/tex] 200
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A certain number is multiplied by 7, and 4 is taken from the product. Finally, the difference is divided by 9, resulting in 5. Find the initial number.
Answers
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials..
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a brown marble from the bag.
The theoretical probability, P(brown), is 50%, and the experimental probability is 25%.
The theoretical probability, P(brown), is 50%, and the experimental probability is 22.5%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 13.0%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
Answers
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
In this question, we have been given there are 10 brown, 10 black, 10 green, and 10 gold marbles in bag.
The theoretical probability of pulling a brown marble from the bag would be,
P = 10/40
P = 0.25
P = 25%
A student pulled a marble, recorded the color, and placed the marble back in the bag.
The frequency of each color pulled during the experiment after 40 trials is:
Brown 13
Black 9
Green 7
Gold 11
So, the experimental probability of pulling a brown marble from the bag would be,
P = 13/40
P = 0.325
P = 32.5 %
Therefore, the theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
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Answer: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
Step-by-step explanation: :)
Please help me complete this flowchart proof. The correct answer gets brainiest
Answers
The flowchart that is used to prove GR ║ F_K is presented as follows;
∠RND and ∠FDP are supplementary ⇒ ∠RND + ∠FDP = 180°
Given [tex]{}[/tex] Definition of supplementary
∠KDN ≅ ∠FDP [tex]{}[/tex] ⇒ ∠KDN = ∠FDP
Vertical angles are congruent[tex]{}[/tex] Definition of congruent angles
∠RND and ∠KDN are same side interior angles [tex]{}[/tex] ⇒∠RND + ∠KDN = 180°
Definition of same side interior angles[tex]{}[/tex] Substitution property
[tex]{}[/tex] GR ║ F_K
Same side interior angles formed between parallel lines that have a common transversal are supplementaryWhat are the relationships between the angles formed between parallel lines that have a common transversal?The relationships between the angles formed by a transversal and two parallel lines are;
Corresponding angles are congruentSame side interior angles are supplementaryLinear pair angles are supplementaryVertical angles are congruentAlternate interior angles are congruentAlternate exterior angles are congruentDefinition of congruency;
Two lines, shape or figure are said to be congruent if they have the same size and shape.
Supplementary angles;
Supplementary angles are angles that have a sum of 180°
Substitution property of equality
The substitution property sates that if an expression a = b, then the expression b can replace a in any equation and the equation will remain valid.
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Rewrite the expression in simplest form.
(x^3 + 2x^2 -x) -(x^3 + 2x^2+6)
Answers
Hope this helps!! :]
Do I need to apply the chain rule when I derive [ln(g(x))]^2?
Answers
To solve the given derivative we need to apply the chain rule.
Given that, [ln(g(x))]².
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
The chain rule is a formula that expresses the derivative of the composition of two differentiable functions [tex]f[/tex] and [tex]g[/tex] in terms of the derivatives of [tex]f[/tex] and [tex]g[/tex].
Find the derivative using the chain and power rules.
ln(g²x²)/x
Therefore, to solve the given derivative we need to apply the chain rule.
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What is your country name?
Answers
Claire has sold 8 candy bars and sells 5 more each day. Ayden has sold 20 candy bars and sells 3 more each day. How many days (d) will it be before Claire sells as many candy bars (c) as Ayden.
Answers
It will take 7 days for Claire to sell as many candy bars as Ayden
Claire has sold 8 candy bars and sells 5 more each day
The first term = 8
Common difference = 5
nth term is = a+(n-1)d
= 8 +(n-1)5
= 8 + 5n - 5
= 3 +5n
Ayden has sold 20 candy bars and sells 3 more each day
The first term = 20
Common difference = 3
nth term = a+(n-1) d
= 20 +(n-1)3
= 20 + 3n -3
= 17 + 3n
Then,
3 + 5n = 17 + 3n
5n - 3n = 17 - 3
2n = 14
n = 14/2
n = 7
Hence, it will take 7 days for Claire to sell as many candy bars as Ayden
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Divide. If the polynomial does not divide evenly, include the remainder as a fraction.
2
(13q² +82q - 55) ÷ (q + 7)
Answers
The division of the given polynomial is [tex]13q - 9 + \frac{8}{q+7}[/tex].
What is the quotient of polynomials?
Any quotient of polynomials a(x)/b(x) can be expressed as q(x)+r(x)/b(x), where r(x) is a real number and b is a real number (x). For instance, x-2+3 can be used to represent (x2-3x+5)/(x-1) (x-1).
We have,
[tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]
By dividing,
[tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)} / \frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]
[tex]= 13q + \frac{-9q - 55)}{ (q + 7)}[/tex]
[tex]\frac{-9q - 55}{q+7} / \frac{-9q - 55}{q+7}[/tex]
[tex]= 13q - 9 + \frac{8}{q+7}[/tex]
Hence, the division of the given polynomial is [tex]13q - 9 + \frac{8}{q+7}[/tex].
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BD = 5, CX = 3, CD = 5
what does BC equal
Answers
Answer:
BC = 6
Step-by-step explanation:
since BD = CD then Δ BCD is isosceles.
the line a through D is a perpendicular bisector of BC, then
BX = CX = 3 , so
BC = BX + CX = 3 + 3 = 6
John bought a pair of jeans on sale for $10 off. The original price of the jeans was $45. What was the sale price of the jeans?
Answers
Answer:
$35
Step-by-step explanation:
All you have to do is subtract 10 from 45 because it was $10 off and the original price was $45.
What numbers are elements? -7, -4, 2, 14, 21, 34, 42
Answers
The answer is [14, 42].
The number 14 is even.
7 x 2 = 14
An even number, 42.
7 x 6 = 42
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Use the properties of congruent triangle to find the value of x and y. Be sure to show all your work
Answers
Answer:Angles in a triangle may or may not be congruent.
The values of x and y are 90 and 47, respectively.
From the figure, we have:
This means that, angle x is a right-angle.
So, we have:
Triangle ABC is an isosceles triangle.
So, we have:
The measure of y is then calculated as:
--- sum of angles in a triangle
This gives
Subtract 137 from both sides
Hence, the values of x and y are 90 and 47, respectively.
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Step-by-step explanation:
The population of Minnesota in thousands, t years since 2000 can be represented by P=37t+4934. (T,P)=
A) Determine the P-intercept and explain its meaning in terms of the problem. (T,P) =
B) Determine the t-intercept and explain its meaning in terms of the problem. (T,P)
Answers
Answer A ; 4934 is the P-intercept. which indicates that 4934 people called Minnesota home in 2000.
Answer B ; T-intercept is -4934/37, or approximately -133. This indicates that Minnesota had a population of 2000–133 in 1867.
Answer A : P=37t+4934 can be used to represent Minnesota's population in thousands over the t years after 2000.
P-intercept is the P value at time t=0.
P=37*0+4934\sP=0+4934\sP=4934
So, 4934 is the P-intercept. which indicates that 4934 people called Minnesota home in 2000.
Answer (B) : The term "t-intercept" refers to the value of the function t when P=0 0=37t+4934 -4934=37t divide by 37 -4934/37=t -133.351351351 = t
Hence T-intercept is -4934/37, or approximately -133. This indicates that Minnesota had a population of 2000–133 in 1867.
P=37t+4934 P-intercept means the value of P at t=0 P=37*0+4934 P=0+4934 P=4934
Given that Minnesota's population in thousands, t years since 2000, it can be expressed by the equation:
So, 4934 is the P-intercept. which indicates that 4934 people called Minnesota home in 2000.
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Find all real numbers x such that
(3^x - 27)^3 + (27x - 3)^3 = (3x + 27x - 30)^3
Answers
All the real numbers x in the expression such that (3x - 27)³ + (27x - 3)³ = (3x + 27x - 30) is x = 1 .
In the question ,
it is given that the expression is
(3x - 27)³ + (27x - 3)³ = (3x + 27x - 30)
By using the identity a³ + b³ [tex]=[/tex] (a + b)(a² - ab + b² )
we get ,
[(3x - 27 + 27x - 3)] × [(3x - 27)² - (3x - 27)(27x - 3) + (27x - 3)² ] = 30x - 30
(30x - 30)×[(3(x - 9))² - (3(x - 9) × 3(9x - 1)) + (3(9x - 1))²] = 30x -30
using the identity (a-b)² [tex]=[/tex] a² -ab + b²
(30x - 30) × [9( x² - 18x + 81) - (9(9x² - 82x + 9)) + (9(81x² - 18x + 1)) = 30x-30
9(30x - 30)×[x² - 18x + 81 - 9x² + 82x - 9 + 81x² - 18x + 1] = 30x - 30
270×(x - 1)×[ 73x² + 46x + 73] = 30(x - 1)
taking (x-1) terms to LHS ,
we get
(270 - 30)×(x - 1)[ 73x² + 46x + 73 ] = 0
(240) (x - 1) [ 73x² + 46x + 73 ] = 0 ....because 270-30 = 240
Dividing both sides by 240
we get ,
(x - 1) [73x² + 46x + 73] = 0
So , either x - 1 = 0 or 73x² + 46x + 73 = 0
on solving 73x² + 46x + 73 = 0
we get the discriminant of 73x² + 46x + 73 a negative number , so it cannot have real root .
hence x -1 = 0
x = 1
Therefore , the only real solution is x = 1 .
The given question is incomplete , the complete question is
Find all real numbers x in the expression such that (3x - 27)³ + (27x - 3)³ = (3x + 27x - 30) ?
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8) I bought 4 baseball cards for y dollars each and 3 card holders for $2.50
each. I paid a total of $19.50. What is the cost per baseball card?
PROVE IT!! SHOW YOUR WORK!!!!!
A) $3 B) $4 C) $5.50 D) $6
Answers
Answer:
$3
Step-by-step explanation:
Total of all = $19.50
3 Card holders total = $7.50
4 Baseball card total = ?
We know that 19.50 is the sum of the holders and cards together so we subtract $7.50 from $ 19.50.
$19.50-$7.50=$12 for ALL four baseball cards
We know that 4 baseball cards are $12, but if we DIVIDE 12 by four, we get the individual price per card.
12/4 = $3
What is the domain of the following relation?
a. {-3, -1, 1, 4, 5}
b. {-5, 0, 2, 6}
c. {-3, -5, 0, 2, 4, 5, 6}
d. there is no domain
Answers
The domain of the relation in the diagram below is: a. {-3, -1, 1, 4, 5}.
What is the Domain of a Relation?A relation has a set of domain elements, which are all the inputs of the relation that are mapped to a set of range elements, which are all the corresponding outputs of the relation.
Given the relation as shown in the diagram that is attached below showing a mapping, the set of input values is {-3, -1, 1, 4, 5}, while the set of output values is {-5, 0, 2, 6}.
Therefore, {-3, -1, 1, 4, 5} is the domain of the relation because it is the set of all input values, while the range of the relation is {-5, 0, 2, 6}, because it is the set of all output values that corresponds to the input values.
The domain is therefore: a. {-3, -1, 1, 4, 5}.
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Current Attempt in Progress
Monty Corp. purchased a new machine on October 1, 2022, at a cost of $124,000. The company estimated that the machine will have
a salvage value of $15,000. The machine is expected to be used for 10,000 working hours during its 5-year life.
(a)
Compute the depreciation expense under straight-line method for 2022.
Depreciation expense $
2022
Answers
The depreciation expense under the straight-line method for 2022, for Monty Corp., is $5,450.
What is the straight-line depreciation method?Under the straight-line depreciation method, one of the cost-recovery methods, the depreciable amount of an asset is divided by its estimated useful life.
The quotient is the depreciation expense for each year. However, if the asset is not used for a full year, the depreciation expense is prorated according to the number of months or days that the asset is in use.
Note that the depreciable amount is the difference between the cost of the asset and its salvage value.
Cost of new machine = $124,000
Purchase date = October 1, 2022
Estimated salvage value = $15,000
Depreciable amount = $109,000 ($124,000 - $15,000)
Estimated useful life = 5 years
Estimated working hours = 10,000 hours
Depreciation method = Straight-line
Annual Depreciation Expense = $21,800 ($109,000/5)
October 1, 2022, to December 31, 2022, = 3 months
Depreciation expense for 2022 = $5,450 ($21,800 x 3/12)
Thus, using the straight-line method, Monty Corp. will record a depreciation expense of $5,450 for the new machine it purchased on October 1, 2022.
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what is the solution of the linear-quadratic system of equations y=x^2+2x-3 y=2x+1
Answers
Answer:
(x, y) = {(-2, -3), (2, 5)}
Step-by-step explanation:
You want to solve the system of equations y=x²+2x-3 and y=2x+1.
SolutionThe two expressions for y can be equated, and the resulting equation put in standard form.
x² +2x -3 = 2x +1
x² -4 = 0 . . . . . . . . . . subtract (2x+1)
(x -2)(x +2) = 0 . . . . . factor
Values of x that make the factors zero are 2 and -2.
Corresponding values of y are ...
y = 2x +1 = 2(2) +1 = 5
y = 2(-2) +1 = -3
Solutions are ...
(x, y) = (2, 5)(x, y) = (-2, -3)Use the Remainder Theorem to evaluate P(c).
P(x) = x4 + 7x³ – 6x – 11,
-
X
f(-1) =
[
C = -1
Answers
Answer:
[tex]-11[/tex]
Step-by-step explanation:
[tex]P(-1)[/tex] is the remainder when [tex]P(x)[/tex] is divided by [tex]x+1[/tex].
[tex]\frac{x^4 + 7x^3 - 6x-11}{x+1}=x^3 + 6x^2 - 6x-\frac{11}{x+1}[/tex].
The remainder is [tex]-11[/tex], so [tex]P(c)=-11[/tex].
absolute value 2x - 6 less than 0
Answers
The solution set for the inequality is (-3, 3)
How to solve the absolute value inequality?Here we have the absolute value inequality
|2x| - 6 < 0
To solve this, we need to isolate the variable, which in this case is x.
Adding 6 in both sides we get:
|2x| -6 + 6 < 0 + 6
|2x| < 6
This can be decomposed in the inequality:
-6 < 2x < 6
Now to competely solve the inequality, we will divide both sides by 2, so we get:
-6/2 < 2x/2 < 6/2
-3 < x < 3
So the solution set is (-3, 3)
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At an arcade, a book of 20 tickets costs $5, a book of 30 tickets costs $7, and a book of 50 tickets costs $10. Would a graph of the relationship between price and number of tickets in a book be a straight line? Explain.
Answers
Answer:
yes
Step-by-step explanation:
Which phrase represents the algebraic expression for n – 4?
A. The quotient of a number and four.
B. Four less than a number.
C. Four minus a number.
D. Four more than a number
Answers
The phrase that represents the algebraic expression n - 4 is option b four less than a number.
Given,
The algebraic expression; n - 4
We have to find the phrase that represents the given algebraic expression.
Algebraic expression;
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
An algebraic expression can be categorized into different categories depending on how many terms it contains: polynomial, quadrinomial, trinomial, monomial, and binomial.
So,
n - 4
That is,
4 is less than from a number
Therefore,
The phrase that represents the algebraic expression n - 4 is option b four less than a number.
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Answer:
the answer is b
Step-by-step explanation:
Plot a point that is in the solution region of this inequality.
y>x-3+8
Answers
The point (-6,6) is in the solution region of the inequality and is plotted in given below graph.
Given,
Equation -> y > x - 3 +8
y > x + 5
Lets take a point A(-6,6)
Putting the value in equation,
6 > -6 + 5
6 > -1
which is true.
Hence, A(-6,6) lies in the region of the inequality.
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Comparing Marbles:
Red balloons float purple marbles at a ratio of 12: 4.
Red balloons float green marbles at a ratio of 15: 6.
Which is heavier: a purple marble or a green marble?
Answers
The marble that is heavier based on the ratio is purple marble.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.
Red balloons float purple marbles at a ratio of 12: 4. This will be:
= 12/4
= 3
Red balloons float green marbles at a ratio of 15: 6. This will be:
= 15/6
= 2.5
In this case, the purple marble is heavier as 3 is more than 2.5.
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