The two equations with infinitely many solutions are the ones in options B and C.
−76x+76=−76x+7676x+76=76x+76Which of the given equations has infinitely many solutions?An equation only has infinitely many solutions if we have a true equation that does not depend of x.
For example, if you look at option B, we have:
-76x + 76 = -76x + 76
We have the same expression in both sides, if we subtract it in both sides we get:
0 = 0
This is true, and does not depend of x, so this equation has infinitely many solutions.
The same thing happens for equation C.
76x+76=76x+76
Where we have the same thing in both sides.
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1/4t = 1/3t + (-16)
pls solve t and show steps if possible
Answer:
t = 192
Step-by-step explanation:
1/4t = 1/3t + (-16)
1 1
-------t = -------t - 16
4 3
1(3) 1(4)
-------t = -------t - 16
4(3) 3(4)
3 4
-------t = -------t - 16
12 12
3 4
-------t = -------t - 16(12)
( 12 12 ) 12
3t = 4t - 192
-4t -4t
---------------------
-t = -192
÷-1 ÷-1
---------------
t = 192
I hope this helps!
Select the correct answer. Consider the graph of f(x) given below. The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)? A. g(x) = f(x - 5) B. g(x) = f(x) - 2 C. g(x) = f(x) - 5 D. g(x) = f(x + 2)
PLEASE OFFER ME YOUR ANSWER, I ASK OF YOU...PLS
The function that could represent g(x) is (c) g(x) = f(x) - 5
How to determine the function g(x)?The figure of the graph that completes the question is added as an attachment
From the attached graph, we have the equation of the function to be
y = f(x)
Also, the graph of the function f(x) has its intercept to be
y-intercept of f(x) = 3
From the question, we have
y-intercept of g(x) = -2
Subtract the intercepts
Difference = y-intercept of g(x) - y-intercept of f(x)
So, we have
Difference = -2 - 3
Evaluate
Difference = -5
The function g(x) is then represented as
g(x) = f(x) + Difference
So, we have
g(x) = f(x) - 5
Hence, the function g(x) is g(x) = f(x) - 5
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Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.
ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°
ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°
Given,
Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.
What are unique triangles?
Unique triangles are triangles that are different based on their configuration, which derives from the positioning of the given parameters to correspond with different congruency requirement.
The conditions for the congruency of two triangles are;
SSS: The Side-Side-Side rule; two triangles are congruent if all three sides of one triangle are congruent to the three sides of the other triangle
SAS: The Side-Angle-Side rule; two triangles are congruent if two sides and the included angle of one are congruent to two sides and an included angle in the other triangle
ASA: The Angle-Side-Angle rule; two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and an included side of the other triangle
SAA: The Side-Angle-Angle rule; Two triangles are congruent if two angles and an a non included side of one triangle are congruent to two angles and the non included side of the other triangle.
The configuration of the unique triangles can therefore, be ASA and SAA, which gives the triangles;
ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°
ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°
Please see attached drawings of the two unique triangles
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A technical machinist is asked to build a cubical steel tank that will hold 415 L of water.Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.001 m.
we have
1 cubic meter = 1000 L
x cubic meter = 415 L
then:
[tex]\begin{gathered} 1000\times x=415\times1 \\ 1000x=415 \\ \frac{1000x}{1000}=\frac{415}{1000} \\ x=0.415 \end{gathered}[/tex]The volume of a cube with length x is:
[tex]\begin{gathered} x^3=0.415 \\ \sqrt[3]{x^3}=\sqrt[3]{0.415} \\ x=0.746 \end{gathered}[/tex]answer: The smallest possible inside length of the tank is 0.746 m
is 12 an integer? Im getting confused answers
Answer:
Yes 12 is an Integer
Step-by-step explanation:
12 is a whole number that can be written without a fractional component, thus 12 is an integer.
Simplify nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight. eleven square root of two minus five square root of seven eleven square root of four minus five square root of fourteen six square root of five six square root of nine
Squares are the numbers that are produced when a value is multiplied by itself.
If expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex] then the value exists [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex].
What is meant by square root?The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.
Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.
The original number can be attained by multiplying the square root of an integer by itself.
Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.
Let the expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
Now, [tex]$\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$[/tex]
[tex]$\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$[/tex]
therefore [tex]9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
simplifying the given expression, we get
[tex]$=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$[/tex]
[tex]$=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$[/tex]
[tex]$=11 \sqrt{2}-5 \sqrt{7}$[/tex]
Therefore, the correct answer is option a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
The complete question is:
Simplify [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
b) [tex]$11 \sqrt{4}-5 \sqrt{14}$[/tex]
c) [tex]$6 \sqrt{5}$[/tex]
d) [tex]$6 \sqrt{9}$[/tex]
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help, please! ♡ (photo attached)
The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.
How to simplify a rational equation by algebra properties
In this case we find a rational equation whose numerator and denominator are polynomials, which must be simplified by using algebra properties. The complete procedure is now shown:
(9 · x - 6)² / (2 · x⁴ + 4 - 2 · x⁴ - 1) Given
(81 · x² - 108 · x + 36) / (3) Perfect square binomial / Associative, commutative and modulative properties / Existence of additive inverse /Definition of subtraction
27 · x² - 36 · x + 12 Addition and subtraction of fractions with same denominator / Associative and commutative properties / Definition of division
The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.
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Juanita has a part-time job that pays $12/hour and works about 50 hours every month. Her
withholdings are Social Security. (6.2%), Medicare (1.45%) and federal income tax (10%). What
is her approximate net pay?
a. $120
b. $500
c. $600
d. $700
The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.
Given that, Juanita has a part-time job that pays $12/hour and works about 50 hours every month.
What is the net pay?Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.
Now, total money earned in a month
= 12 × 50 = 600
Now
6.2% of 600 = $37.2
= 600 - 37.2 = $562.8
1.45% of 562.8 = $8.1606
= 562.8 - 8.1606 = $554.6394
10% of 554.6394 = $55.46394
= 554.6394 - 55.46394 = $499.17546
Total deductions = $499.17546
So, net pay = grass pay - deductions
= 600 - 105.9
= $499.17546
The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.
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What's the number of possible outcome when a coin is tossed four times
Answer:equal
Step-by-step explanation: no number but equal as it is tossed 4 times
Answer:
16
Step-by-step explanation:
The number of possible outcomes at each coin toss = 2.
The total number of possible outcomes after 4 times = 2⁴ = 16.
A train ticket in a certain city is 3.00. People eho use the train also have the option of purchasing a frequent rider pass for 18.75 each month. With the pass, each ticket costs only 2.25. Determine the number of times in a month the train must be used so that the total monthly cost without the pass is the same as the total monthly cost with the pass.
The number of times for which the train must be used so that the monthly cost without the pass is same as with the pass is; 6.25 times.
How to solve Word Problems using algebraic expressions.It follows from the task content that the regular train ticket costs, 3.00.
Therefore, the cost for travelling x times with the month is; 3x.
On this note, for the total monthly cost without the pass to be same as that with the pass; the equation which must hold is;
3x = 18.75
x = 18.75/3
x = 6.25 times.
Therefore, after taking the train 6.25 times, the cost without the pass is same as that with the pass.
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A tennis racket sells for $54.At the spring clearanceevent, the price is 30% lessthan the original. What isthe sale price?
We have
tennis racket price $54
Firs we need to obtain the 30 %
54*.30=16.2
then in order to know the sale price we need to substract the 30% of the original price
54-16.2=37.8
the sale price is $37.8
Find the value of x in each case.
Not rlly sure how to make the equation, i tried it a couple times and got the answer wrong
Pls help and ill reward Brainly thing
Last night, Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael. If Dayja read 84 pages, how many pages did Luis, Dayja, and Michael read all together?
Answer:
Total pages read = 279 pages
Step-by-step explanation:
Let L, D, and M stand for the pages read by Luis, Dayja, and Michael, respectively.
We learn that:
L = 1.75D, [Luis read 75% more pages than Dayja]
D = 1.75M, and [Dayja read 75% more pages than Michael]
D = 84 [Dayja read 84 pages]
We want the sum of L, D, and M
Total pages = L + D + M
We have three equations and 3 unknowns. We should be able to find a solution by rearranging and substituting.
Total pages = L + D + M
We can substitute L=1.7D and rearrange D = 1.75 M to M = D/1.75
Total pages = L + D + M
Total pages = 1.7D + D + D/1.75
Total pages = D(1.7 + 1 + 1/1.75) [Isolate the D, for optional simplification]
Total pages = D(3.271)
We know D = 84, so:
Total pages = 84(3.271)
Total pages = 274.8
We'll round that to 275 pages.
Check:
L = 1.75D: L read 1.75*275 or 147 pages
D read 84 pages
D = 1.75M, or M = D/1.75; M read 84/1.75) or 48 pages
Total pages read = 147 + 84 + 48
Total pages read = 279 pages
Question - Write an equivalent expression for -3.1 ^ 4 x * -3.1 ^ 2 x + 7
Does anyone have an expert verified answer for this?
The expression -3.1^4x * -3.1^2x + 7 has an equivalent of 887.503681x^2 + 7
How to determine the equivalent expressionFrom the question, the expression is given as
-3.1^4x * -3.1^2x + 7
Evaluate the exponents in the above expression
So, we have the following equation
-3.1^4x * -3.1^2x + 7 = 92.3521x * 9.61x + 7
Evaluate the products in the above expression
So, we have the following equation
-3.1^4x * -3.1^2x + 7 = 887.503681x^2 + 7
Hence, the equivalent expression of -3.1^4x * -3.1^2x + 7 is 887.503681x^2 + 7
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Given the figure below, determine the angle that is an alternate interior angle with respect to. 1. To answer this question, click on the appropriate angle.
In this case, the alternate interior angles are for example angles 6 and 3 because they are on the inner side of each of the lines (m and l) but on opposite sides of the transversal (t).
m∠6 = m∠3
or
m∠4 = m∠5
two planes are flying torwards each other. in 45 minutes, the two planes will be 200 miles apart. in 1 hour, plane A will pass plane B. How far apart are the planes now.
800 miles is going to be the distance that separates the two aircraft. The distance between the two airplanes will be 1,300 kilometers at the very least.
What is the distance?It is important to keep in mind that the two aircraft's combined speed will be equal to the sum of their separate speeds when calculating their overall speed. In addition, the pilots of the two aircraft have one hour to find each other.
According to the information that was provided, the distance that separates the aircraft after they have flown for forty-five minutes is two hundred miles. As a result, the following will constitute the remaining distance:
= 1 hour - 45 minutes = 15 minutes.
When this occurs, the distance between the planes will be as follows:
= 200/15 × 60
= 200 × 4
= 800 miles
As a result, there will be a gap of 1300 kilometers between the two aircraft.
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What is the value of x?
Answer:
x=62
Step-by-step explanation:
X=62 because all angles of a triangle should add up to 180 degrees no matter what. All you have to do is subtract the already known angles in the triangles from 180 to receive your x value. 180-65-53=x 180-65-53=62.
-Hope this helps
Which of the following is an example of a set of like terms ??
2. >>>>>>>b {18x,-x,21x} is an example of like terms because they both hold the same variables.
4.>>>>>>
[tex] = - 7(2x - 3) \\ = - 7(2x) - 7( - 3) \\ = - 14x + 21[/tex]
ATTACHED IS THE SOLUTION
A bank features a savings account that has an annual percentage rate of r=2.8% with interest. compounded quarterly. Benicio deposits $8,000 into the account.
Explanation
From the given question
We are given the formula to compute the amount that a sum of $8000 compounded quarterly will yield after time t at a rate of 2.8%
The formula is given by
[tex]A(t)=a(1+\frac{r}{k})^{kt}[/tex]Part A
[tex]\begin{gathered} a=initial\text{ deposit= \$8000} \\ \\ k=number\text{ of times compounded in a year = 4} \\ \\ r=2.8\text{ \% =0.028} \\ \\ \end{gathered}[/tex]part B
the amount in the account after 7 years will be
[tex]\begin{gathered} A(t)=8000(1+\frac{0.028}{4})^{4\times7} \\ \\ A(7)=\text{ \$}9725.57\text{ } \end{gathered}[/tex]The amount that will be in the account after 7 years will be $9725.57
Part C
APY is given by
In our case we have
[tex]\begin{gathered} APY=(1+\frac{r}{k})^k-1 \\ APY=\left(1+\frac{0.028}{4}\right)^4\:-1 \\ APY=1.02829-1 \\ APY=0.02829 \end{gathered}[/tex]Hence, we will have the APY as
[tex]\begin{gathered} APY=0.02829\times100\text{ \% } \\ APY=2.829\text{ \%} \end{gathered}[/tex]Hence, the APY is 2.829%
The rental price of a dacha was $9000. At the end of each month
the price is increased by 6%.
a) Find the price of the house after 1 month.
b) Find the price of the house after 3 months.
c) Find the price of the house after 10 months
a) The price (amount) of the house after 1 month = $9540
b) The price (amount) of the house after 3 months = $10719.14
c) The price (amount) of the house after 10 months = $16117.629
a ) How to find the rental price of the house after 1 month ?
The rental price of a dacha = Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 1
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]
The rental price of the house after 1 month = $9540
b ) How to find the rental price of the house after 3 months ?
The rental price of a dacha = Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 3
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]
The rental price of the house after 3 months = $10719.14
c ) How to find the rental price of the house after 10 months ?
The rental price of a dacha =Principle = $9000
Percentage increase in price = r = 6%
Number of months = n = 10
Amount of a compound interest is given by,
[tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]
The rental price of the house after 10 months = $16117.629
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A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. Is it a right triangle?
Based on the lengths of the sides of the triangle, we can infer that this is NOT a right triangle.
How to find a right triangle?A right angled triangle would obey the Pythagoras Rule which is that the square of the hypotenuse (longest side) will be the sum of the squares of the other sides of the triangle.
This means that for this to be a right triangle, it needs to obey the function:
45 ² = 35 ² + 30 ²
Solving gives:
2,025 ≠ 2, 125
This shows that the triangle is not a right triangle.
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It is not a right-angle triangle since 2125 ≠ 2025 meant that it did not conform to Pythagoras' theorem's specifications.
This kind of query creates a right-angled triangle that Pythagoras' theorem can resolve.
What is Pythagoras' theorem?In a right-angled triangle, the square of the greatest side is equal to the sum of the squares of the smaller two sides.
Given, There are three sides to a triangle, each measuring 30 kilometers, 35 kilometers, and 45 kilometers.
∴ 30² + 35² = 45².
900 + 1225 = 2025.
2125 ≠ 2025.
Due to the fact that it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.
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PLS
Natasha has a photo of a lasagna dish she made, which she wants to post to various
websites. The original image has a width of 300 pixels and a height of 450 pixels.
Consider each set of new dimensions or scale percents that show adjustments to this
original image. Describe how the image changed and whether the new image is
similar to the original. Show your work and explain your reasoning.
New image: 35% width, 35% height
As both the width and height of the new image are 35% of the width and height of the original image, the aspect ratio is maintained and the new image is similar to the original image.
What is a Scale Factor?A scale factor is defined as the ratio of an object's original scale to that of a new one, considering the different depictions of that object (bigger or smaller)
Given:
The dimensions of the original image are a width of 300 pixels and a height of 450 pixels.
The dimensions of the New image have 35% width and 35% height.
Width = 0.35 × 300 = 105
Height = 0.35 × 450 = 157.5
Scale factor = New Dimension/Original Dimension
Scale factor of Height = 157.5/450 = 0.35
Scale factor of width = 105/300 = 0.35
Therefore, the new image is neither scaled down nor scaled up and is the same as the original image.
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during a span of 2 hours , lalia played her video games for 50 minutes . what percentage of time was spent on the game
Total time = 2 hours
Time playing video games = 50 minutes
We have to write an equation:
Total time (2hours) multiplied by the percentage in decimal form (x) must be equal to 50 minutes
Time must be in the same unit ( minutes)
since 60 minutes =1 hour
2 hours = 2 (60) =120 minutes
Back with the equation:
120 x = 50
Solving for x
x = 50/120
x = 0.42
In percentage form:
0.42 x 100 = 42%
Which pair of statements about the lengths of two sides of the triangle is true? 10 9 8 D (8,7) 7 л д) 4 3 2 1 X F(6, 1) 2 3 4 5 6 E (8.1) 8 9 10 1 7 O A. The side length between Dand Eis 7 units. The side length between Eand Fis 2 units. O B. The side length between D and Eis 6 units. The side length between E and Fis 2 units. O C. The side length between D and Eis 2 units. The side length between E and Fis 6 units. O D. The side length between D and Eis 8 units. The side length between Eand Fis 1 units.
Answer:
Choice B.
Explanation:
The side length is the distance between the vertices of the triangle given.
the probability of being satisfied with a product purchased online is 0.555. if you buy 8 products online, what is the probability that you will be satisfied with 3 or more of the purchased products? (round your answer to 3 decimal places if necessary.)
The probability that you will be satisfied with 3 or more of the purchased products is 0.916
Given that,
The chance of being pleased with an internet purchase is 0.555. if you purchase 8 items online
Solution -
let X denote the no of success of
Purchased product online
X ~ B(n,p)
n = 8
P= 0. 555
a = 1 - 0 .555 = 0.445
P ( X = x) = [tex]nc_{x} b^{x} a^{n-x}[/tex]
P ( X = x)= [tex]8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]
P ( X>=3)= [tex]\lim_{3 \to 8} 8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]
P ( X>=3)) = 0.91614
=0.916
Therefore we can conclude the probability that you will be satisfied with 3 or more of the purchased products is 0.916
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Pls Help will give brainliest
Anita earns 60 points every time she shops at a grocery store. She needs a total of 2,580 points to receive a free prize. So far, she has earned 480 points. How many more times will Anita have to shop at the grocery store in order to earn the additional points she needs for a free prize?
Answer:
35Step-by-step explanation:
So she needs 2580 points
she has already earned 480, so let's subtract that
that leaves up with 2100 more points
she earns 60 points every shop
so lets divide 2100 by 60
2100÷60=
35
Anita will have to shop at the grocery store 35 more times to earn the additional points she needs for a free prize.Answer:
43 total ,35 more times need to get 2,580
Step-by-step explanation:
2580:60=43
60x8=480
43-8=35
Beth and 8 of her friends are going bowling Saturday. Each game cost $x plus an additional $3.25 to rent shoes. Write an expression to represent the total cost of an afternoon of bowling if four friends bring their own shoes.
Answer:
9*X+5*3.25
Step-by-step explanation:
So, total 9 person; 4 person have their own shoe.
Cost for game = 9*X;
Cost for shoe = 5*3.25;
So the total cost = 9*X+5*3.25
please help math is an absolute pain
Answer: 3/5 cm
Step-by-step explanation:
Let the length of the base be x. Then, using the formula for the area of a triangle,
[tex]\frac{3}{25}=\frac{1}{2} \cdot \frac{2}{5} x\\\\\frac{3}{25}=\frac{1}{5}x\\\\x=\frac{3}{5}[/tex]
in Italy the leaning Tower of Pisa currently leans at 13 ft. off the vertical. the tower is 183 ft tall. what is the angle of inclination
The required inclination of the tower of Pisa as 85.95°.
Given that,
in Italy the leaning Tower of Pisa currently leans at 13 ft. off the vertical. the tower is 183 ft tall. what is the angle of inclination is to be determiend.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
base length is 13 ft,
Hypotenuse length of the tower = 183
According to the question,
Cosx = 13/ 183
x = 85.98°
Thus, the required inclination of the tower of pisa as 85.95°.
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Jenna buys three boxes of cocoa.
She gives one box to Keanu and one box to Jacoby.
What fraction of cocoa did Jenna give to her friends?
Answer: 2/3
Jenna had 3 boxes of cocoa and gave away 2, for each friend the fraction is 1/3 therefore 1/3 +1/3 =2/3.... the final fraction is 2/3.
Answer: 2/3
Step-by-step explanation:
total, Jenna had 3/3, then she gave 1/3 to two of her friends. Which makes the total boxes 2/3 of what she gave away with a remaining of 1/3. (1 box of the three boxes)
