Answer:
Step 1: 14x − 21 = 1; Step 2: 14x = 22
Explanation:
7(2x−3)=1
Step 1: Simplify both sides of the equation
7(2x−3)=1
(7)(2x)+(7)(−3)=1(Distribute)
14x+−21=1
14x−21=1
Step 2: Add 21 to both sides
14x−21+21=1+21
14x=22
Step 3: Divide both sides by 14
14x / 14 = 22 / 14
x = 22 / 14: x = 11/7
Answer:
The last option.
Step-by-step explanation:
When distributed, 7 times 2x becomes 14x and 7 times -3 is -21.
Once you add -21 to both sides, 14x is left alone on one side while 22 is on the other
How to do similar polygons?
Answer:
Similar polygon
Step-by-step explanation:
If two polygon similar then the ratio of the corresponding sides is the scale factor.All interior angles are congruent.The dimensions of a rectangular monitor screen are such that it’s length is 4 in. more than it’s width. If the length were doubled and if the width were decreased by 1 in., the area would be increased by 216 in^2. What are the length and width of the screen?
Answer:
14 inches by 18 inches
Step-by-step explanation:
Old rectangular monitor screen:
Width = x in
Length = x + 4 in
Area [tex]=x(x+4)\ in^2[/tex]
New rectangular monitor screen:
Width = x - 1 in
Length = 2(x + 4) in
Area [tex]=(x-1)(2(x+4))=2(x-1)(x+4)\ in^2[/tex]
This area would be increased by [tex]216\ in^2,[/tex] so the area would be equal to [tex]x(x+4)+216\ in^2[/tex]. Hence,
[tex]2(x-1)(x+4)=x(x+4)+216\\ \\2(x^2+4x-x-4)=x^2+4x+216\\ \\2x^2+6x-8-x^2-4x-216=0\\ \\x^2+2x-224=0\\ \\D=2^2-4\cdot (-224)=4+896=900\\ \\x_{1,2}=\dfrac{-2\pm \sqrt{900}}{2}=\dfrac{-2\pm 30}{2}=-16,\ 14[/tex]
The width cannot be negative, so
Width = 14 in
Length = 14 + 4 = 18 in
Solve.
fy=z -8
122+3y=1
Use the substitution method.
०(5, -3)
0 (0, -8)
10 (2, -6)
(4, -4)
Answer: Answer is x = 5, y = -3
(5, -3)
Step-by-step explanation: The instruction is to use the substitution method, and from the first equation,
y = x - 8
This means we replace the value of y in the second equation with x - 8. Hence;
2x + 3y = 1 can now be re-written as
2x + 3(x - 8) = 1
2x + 3x - 24) = 1
5x - 24 = 1
Add 24 to both sides of the equation
5x -24 + 24 = 1 + 24
5x = 25
Divide both sides of the equation by 5
x = 5
Having calculated x as 5, we can now substitute for the value of x in the first equation
y = x - 8 now becomes
y = 5 -8
y = -3
Using the substitution method, we found the solution to be (5, -3), which matches option a.
To solve the system of equations using the substitution method, we'll first solve one equation for one variable and then substitute it into the other equation.
Given:
1. [tex]\( y = x - 8 \)[/tex] (Equation 1)
2. [tex]\( 2x + 3y = 1 \)[/tex] (Equation 2)
From Equation 1, we can solve for y:
[tex]\[ y = x - 8 \][/tex]
[tex]\[ x = y + 8 \][/tex] (Re-arranging)
Now, substitute [tex]\( x = y + 8 \)[/tex] into Equation 2:
[tex]\[ 2(y + 8) + 3y = 1 \][/tex]
Simplify and solve for y:
[tex]\[ 2y + 16 + 3y = 1 \][/tex]
[tex]\[ 5y + 16 = 1 \][/tex]
[tex]\[ 5y = 1 - 16 \][/tex]
[tex]\[ 5y = -15 \][/tex]
[tex]\[ y = -3 \][/tex]
Now, substitute [tex]\( y = -3 \)[/tex] into Equation 1 to find [tex]\( x \)[/tex]:
[tex]\[ x = (-3) + 8 \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution to the system of equations is [tex]\( (x, y) = (5, -3) \)[/tex].
after 2/5 of the kittens were given away, there was k kittens and p puppies left in the pet store. write and algebraic expression in terms of k
Answer:
Algebraic expression in terms of k
k= T- p
Step-by-step explanation:
As
no of kittens left = k
no of puppies left =p
If total left after giving away kittens =T
T = p + k
In terms of k the expression will be
k= T- p
Keywords: Algebra
Learn more about algebra at:
brainly.com/question/3739260 brainly.com/question/13168205 brainly.com/question/9607945#learnwithBrainly
Final answer:
To write an algebraic expression in terms of k, subtract the number of kittens given away from the initial number of kittens. The algebraic expression in terms of k is (3/5)x.
Explanation:
To write an algebraic expression in terms of k, we need to determine the initial number of kittens before any were given away. Let's call this number 'x'. According to the problem, 2/5 of the kittens were given away. This means that (2/5)x kittens were given away, leaving k kittens remaining.
To find the algebraic expression in terms of k, we subtract the number of kittens given away from the initial number of kittens. So the expression is x - (2/5)x = k.
We can simplify this expression by finding a common denominator for the fractions. In this case, the common denominator is 5. So the expression becomes 5x/5 - (2/5)x = k. Simplifying further, we have (3/5)x = k. Therefore, the algebraic expression in terms of k is (3/5)x.
Find the balance in the account after the given period.
$2,200 deposit earning 4.2% compounded monthly, after 1 year
Answer:
2294.20
Step-by-step explanation:
the formula [tex]A = P (1+\frac{r}{n}) ^{nt}[/tex] will show the exponential growth in the account
A = amount in account (how much you'll have after earning interest)
P = the initial amount (how much YOU put in the account)
r = interest rate (in decimal form)
n = the number of times the interests in compounded in one year
t = number of years
plug in numbers into formula
(4.2 will become 0.042 because we need it as a decimal)
(n = 12 because monthly means every month and there is 12 months in a year)
formula will look like [tex]A = 2200 (1+\frac{0.042}{12})^{12(1)}[/tex]
once solved you will get 2294.199616 *round as needed
a number times 45 decreased by 12 is no more than 117
Answer: n*4512 is less than or equal to 117
Step-by-step explanation: n=number N*45=X X=Number more than 117. X decreased by 12 is less than or equal to 117.
pls help I will mark brainlist if correct !! :))
Slope is -3 and a y-intercept of 7
Answer:
y = -3x + 7
Step-by-step explanation:
Answer: y=-3x+7
Step-by-step explanation:
The formula is y=mx+b. M is the equal to the slope and b is equal to the y-intercept. Since they are both given to you, you just fill them in for the variables and it is your answer
Carter plays 5/8 of a basket ball game. The basket ball game is 40 minutes long. Which if the following shows how to find the number of minutes carter plays?
Answer:
25 minutes is how long Carter played
Step-by-step explanation:
To find out how many minutes Carter plays, multiply 40 minutes by 5/8, which results in 25 minutes of playtime.
Explanation:Finding the Number of Minutes Carter PlaysTo determine the number of minutes Carter plays in a basketball game, which is 40 minutes long, when he plays 5/8 of the game, we use multiplication. We multiply the total game time by the fraction of the game played:
40 minutes (total game length) × (5/8) (fraction of the game played)Steps to calculate:
Multiply the numerator of the fraction (5) by the total game time (40 minutes). 5 × 40 = 200.Divide the product by the denominator of the fraction (8). 200 ÷ 8 = 25 minutes.Therefore, Carter plays for 25 minutes of the basketball game.
Find the value of f(-8) if:f(x)=12x-29
Answer:
f=41, 41×(-8)=-328(not so sure so you might want so check with other people again)
Step-by-step explanation:
f(x)=12x-29
Step 1, u bring the x terms over to one side, in this case on the left side. So it becomes:
f(x)-12x=29
Next step is to find the common factor of the x terms
f(x)-12(x)=29
f-12=29
bring the numbers to the right side
f=29+12
so f=41
5. What value of x makes the equation true?
3(x - 2) = 3x + 7
Answer:
There are no values of x that make the equation true.
Step-by-step explanation:
3(x-2)=3x+7
3x-6=3x+7
3x-6+6=3x+7+6
3x=3x+13
Dviding 3x by 3x will equal 1, and 1 does not equal 13.
Answer:
There are no value of x
Step-by-step explanation:
3(x-2) = 3x+7
3x-6 = 3x+7
-6= 7
=7 +6
=13
so we can say that,There are no value of x
Financing a balloon payment under a new fixed rate loan is called a
A reset option
O
B. loan adjustment
O
c. balloon refinance
D. exercise option
Answer:
rest set option
Step-by-step explanation:
What type of association does the graph show between X and Y? A. Linear positive association B.NoNlinear Positive association C.Linear negative association D.Nonlinear negative association?
Answer: A. Linear positive association
Step-by-step explanation:
As the x values increase, so do the y values. this makes the association to be positive because they are both increasing. Additionally if you were to connect all the data points together you would get a straight line, which makes it linear.
Kiran wrote the expression x-10 for this number puzzle: "Pick a number, add -2, and multiply by 5."
Lin thinks Kiran made a mistake.
How can she convince Kiran he made a mistake?
Answer:
Step-by-step explanation:5(x-2)
The correct expression Kiran is trying to write is 5x - 10
How to write expressionKiran:
x - 10
let x = the unknown numberAdd - 2
= x + (-2)
= x - 2
multiply by 5(x - 2)5
5x - 10
Therefore, the correct expression Kiran is trying to write is 5x - 10
Learn more about expression:
https://brainly.com/question/723406
What is the exponents to write the expression of 6×6?
Answer:
6 to the power of 2 or 6 squared
Answer:
6 to the power of 2 or 6 squared
Step-by-step explanation:
Look at the pic and answer
Answer:
Step-by-step explanation:
To find the length of LK, we can use the triangle similarity concept. First, let's compare triangles LJK and LMK. We can see that they share angle L, and we know that LJ = 10 and KM = 7. By comparing the corresponding sides, we can set up the proportion: LK / LJ = KM / KJ Substituting the given values, we have: LK / 10 = 7 / 11 To solve for LK, we can cross multiply and then divide: LK * 11 = 10 * 7 LK * 11 = 70 LK = 70 / 11 So, LK = 6.36 (rounded to two decimal places). Therefore, the answer is not provided in the answer choices.
From the answer choices, we can conclude that LK = d. 70/11.
What is the value?From the figure we are given, we can use the property of corresponding angles to determine the probable value of LK. From the corresponding sides, LK/LJ is equal to KM/KJ. Now, we substitute the given values to have the following:
LK / 10 = 7 / 11
To get the exact value of LK, we cross-multiply as follows:
LK * 11 = 10 * 7
LK * 11 = 70
LK = 70 / 11
So, the value of LK = 70/11.
Learn more about triangles here:
https://brainly.com/question/14285697
#SPJ1
5) Find the equation of a line in slope-intercept form through the point
(3,-4) and perpendicular to the line x + y = 4.
Answer:
y = -x + 4
perp: m = 1
y + 4 = x - 3
y = x - 7
Step-by-step explanation:
Which expression simplifies...
Answer:
see below
Step-by-step explanation:
If suffices to look at the last term. It must simplify to 4/(3w²), so the exponents of z must match in numerator and denominator, and the ratio of constants must reduce to 4/3.
The exponents of z have the right values in choices B and D, but the ratio of constants only matches in choice D. Looking at the rest of choice D, we see that we can factor 6w²z² from both numerator and denominator, then factor 2 from the remaining numerator to make it match the desired form.
[tex]\dfrac{(12w^2z^4-24w^2z^2)}{18w^4z^2}=\dfrac{6w^2z^2}{6w^2z^2}\cdot\dfrac{2z^2-4}{3w^2}=\dfrac{2(z^2-2)}{3w^2}[/tex]
Kevin has an after-school delivering advertising after 9 weeks he had earned a mean of $24 per week how much does he need to earn in the 10th week to increase his mean weekly earnings to $25
Answer:
$34
Step-by-step explanation:
So he earns $24 per week (ima just say p/w to make it shorter) meaning he earned around $216 in total. To get to $25 p/w, you have to get $250 in total from the 10 weeks. So $250 - $216 = $34.
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Can you explained this and give the answer
Answer:
[tex]x^{\frac{3}{7}}[/tex]
Step-by-step explanation:
What is the simplified form of
[tex](\sqrt[7]{x})(\sqrt[7]{x})(\sqrt[7]{x})[/tex]
Applying property of exponents
Remember that
[tex]\sqrt[n]{x^{m}} =x^{\frac{m}{n}}[/tex]
[tex]x^{m}x^{n}=x^{m+n}[/tex]
so
[tex](\sqrt[7]{x})(\sqrt[7]{x})(\sqrt[7]{x})=(x^{\frac{1}{7}})(x^{\frac{1}{7}})(x^{\frac{1}{7}})=x^{(\frac{1}{7}+\frac{1}{7}+\frac{1}{7})}=x^{\frac{3}{7}}[/tex]
Good morning,
which of the following rational functions is graphed below? thanks
Answer:
C.x/(x+5)(x-2)
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
A triangle with the coordinates (6,4), (2,-1), and (-3,5) is translated 4 Units left and rotate 180 degrees about the origin. What are the coordinates of the image.
Answer:
(-2,-4),(2,1), and (7,-5)
Step-by-step explanation:
The given triangle has coordinates (6,4), (2,-1), and (-3,5).
When we translate 4 units left, the we obtain:
(6,4)------>(6-4,4)=(2,4)
(2,-1)----->(2-4,-1)=(-2,-1)
(-3,5)----->(-3-4,5)=(-7,5)
When the resulting figure is rotated 180° about the origin, the coordinates of the final figure becomes
(2,4)------>(-2,-4)
(-2,-1)----->(2,1)
(-7,5)------->(7,-5)
NB: The mapping for 180° rotation is:
(x,y)----->(-x,-y)
what is equivalent to (4xy-3z)^2 and
what type of special product is it?
Answer:
16x2y2 + 9z2 (They are a perfect square trinomial.
Step-by-step explanation:
What is the slope of the line containing the points (3,4) and (-6,10)
Answer:-.6666666667x +6
Step-by-step explanation:
I have a school calculator
Answer:
-2/3 is the slope
Step-by-step explanation:
Slope = y2 - y1/x2 - x1
= 10 - 4/-6 - 3
= 6/-9
=-2/3
What 48 divide by 879
an otterbox was on sale 20% off. if the sale price was $47.99, what was the original price?
Answer:$38.39
Step-by-step explanation:
Original price: $
47.99
Discount percentage:
20
%
Results
Discount:
$9.60
Final Price:
$38.39
Answer:
$59.99
Step-by-step explanation:
"20% off" translates into "80% of original price."
Thus, 0.80p = $47.99, where p is the original price.
Dividing both sides by 0.80 yields:
p = $59.99
Multiply.
(x-6)(5x-4)
O
A. 5x^2-30x + 24
B. 5x^2 - 34x + 24
c. 5x^2 - 26x-24
D. 5x^2 - 30x-24
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x minus 2, y + 2), what will be the coordinates of A prime?
Answer:
A' (-4,0)
Step-by-step explanation:
The complete question is
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x minus 2, y + 2), what will be the coordinates of A prime? On a coordinate plane, triangle A B C has points A(negative 2, negative 2), B(negative 2, negative 4), C(2, negative 4)
we know that
The rule of the translation is
(x,y) -----> (x-2,y+2)
The coordinates of point A (-2,-2)
Applying the rule of the translation to coordinate A
A (-2,-2) ----- A' (-2-2,-2+2)
A (-2,-2) ----- A' (-4,0)
Answer:
The answer is A on edge
Step-by-step explanation:
Explain when you must write the number 1, and when you do not need to.
Answer:
The number 1 is not necessary when expressing powers of one. For example, you needn't write "5" as [tex]5^{1}[/tex].
Step-by-step explanation:
The number 1 is written when it is part of a larger number, as it is significant. It is not necessary to write leading zeros. In scientific notation, trailing zeros are excluded, and the number is written in a form where only non-zero digits appear before the decimal.
Explanation:Understanding when to write the number 1 and when it's not needed depends on the context in mathematics, especially when dealing with significant figures and scientific notation. Generally, all non-zero numbers are considered significant (rule 1), which means that when a value like 1 is part of a larger number, it contributes to the meaning of that number. However, leading zeros do not count as significant (rule 3).
In the case of multiplication by units, like converting from kilograms to grams, we utilize the concept of multiplying by the number 1 to affect the units without changing the value. For example 0.7 kg can be multiplied by 1000/1 (1000 g / 1 kg) to convert to grams. This is because 1000/1 is equal to 1000, indicating multiplication by one does not change the value.
When expressing numbers in scientific notation, it's important to include the non-zero digits only before the decimal point, excluding any trailing zeros. Thus, 1,500,000 would be written as 1.5 x 106, with the power indicating the necessary number of decimal point movements to place it after the first significant digit.
What is 3.68328446 rounded to the nearest hundredths
Answer:
3.68
Step-by-step explanation: