We can get equation B from equation A by Adding the same quantity to both sides. The equations are equivalent and have the same solution.
The equations are:
A : 4x+2 = 6-x
B : 5x+2 = 6
(1) We can get equation B from equation A by adding x to both sides of the equation.
We can verify this.
Add x to both sides of the equation A,
⇒ 4x+2 +x = 6-x+x
⇒ 5x+2 = 6
This is equation B.
So Add the same quantity to both sides of equation A to get equation B.
(2) We just added a same quantity on both sides of equation A. This will not change the equations. So equation A and equation B are equivalent. Also they have same solution.
Equation A: 4x+2=6-x
⇒ 4x+x = 6-2
⇒ 5x = 4
⇒ x = 4/5
Equation B: 5x+2 = 6
⇒ 5x = 6-2
⇒ 5x = 4
⇒ x = 4/5
So both have same solution.
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A marathon is 46,145 yards (about 26 miles) long. If Terrence has run 23,561 yards, estimate by rounding to thousands the number of yards he needs to run to complete the marathon.Terrence needs to run about ______ yards.
Given:
The length of the marathon is L= 46,145 yards.
The length covered by terrence is d = 23,561 yrads.
The objective is to find the remaining distance need to cover by terrence.
To calculate the remaining distance, we will use the relation,
[tex]x=L-d[/tex]On plugging the values in the above relation, we get,
[tex]\begin{gathered} x=46145-23561 \\ =22584\text{ yards} \\ \approx23000\text{ yards} \end{gathered}[/tex]Hence, Terrence needs to run about 23000 yards.
If E is the midpoint of DF
with DE = 9x + 24 and
EF = 18x - 39, then find x
and DF.
Answer:
x=7, DF = 174
Step-by-step explanation:
18x-39=9x+24
9x=63
x=7
:]
if a student scored a 52 on his first test ,make a prediction for his score on the second test .Assume the regression equation is appropriate for the prediction. Round the answer to 2 decimal places.
Solution
We have the following info given:
x: 75,76, 91, 65,48,75,85,62,51,80,94,43
y: 69, 88, 101, 63, 59, 82, 86, 67, 56, 84, 105, 44
After apply OLS (Ordinary LEast Squares) we got the following regression line:
y= 1.0607x + 0.6442
We want to find the best prediction for a student who scored 52 in the first test so we have this:
y= 1.0607* 52 + 0.6442 = 55.80
Then the best prediction for this case is 55.80
Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.) A = 81°, b = 76, c = 39
First, let's find the measure of the third side, using the law of cosine:
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos(A)\\ \\ a^2=76^2+39^2-2\cdot76\cdot39\cdot\cos81°\\ \\ a^2=5776+1521-927.34\\ \\ a^2=6.369.66\\ \\ a=79.81 \end{gathered}[/tex]Now, let's use Heron's formula to calculate the area:
[tex]\begin{gathered} p=\frac{a+b+c}{2}=97.405\\ \\ A=\sqrt{p(p-a)(p-b)(p-c)}\\ \\ A=1463.75 \end{gathered}[/tex]6. The equations of two lines are 6x - y = 2 and 4x - y = -8. What is thevalue of y in the solution for this system of equations?Your answer
The given system of equations : 6x - y = 2 and 4x - y = -8.
6x - y = 2 ( 1 )
4x - y = -8 ( 2 )
for the value of y, use substitution method:
Solve the equation (1) for y :
6x - y = 2
y = 6x - 2
Susbtitute the value of y in the equation ( 2 )
4x - y = - 8
4x - (6x - 2) = - 8
4x - 6x + 2 = - 8
4x -6x = - 8 - 2
-2x = -10
Divide both side by ( -2)
-2x/(-2) = -10/(-2)
x = 5
Substitute x = 5 in the equation ( 1 )
6x - y = 2
6( 5 ) - y = 2
30 - y = 2
y = 30 - 2
y = 28
So, the value of y is 28
Answer : y = 28
Hey can someone please help me with this drag and drop? I’ll give brainliest :)
Lengths of similar triangles and similar polygons are proportional to each other so, answer to the question in image are-
a. ZY=20
b. X=20.8
c. 9miles
What are similar polygons?
similar polygons are the polygons in which all the corresponding angles are same. Hence, they have same shape. The ratio of sides in any two similar polygons are same. This concept of constant ratio of sides is useful in evaluating the length of sides.
a. A/a=B/b=C/c = D/d
WX/HI=ZY/JK
ZY=20
b. X=(2.4×39)/4.5
X= 20.8
c. If 5cm represents 2miles it implies 1cm represents
1cm=2/5
So, 22.5cm will represent
22.5cm=2/5×22.5
22.5cm=9miles
This means that 22.5cm track represents the distance of 9 miles on map
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[tex] \sqrt{25} [/tex]what's the square root
[tex] \sqrt{25} [/tex] ()
what's the square root ?
√25 = 5
because 5*5= 25
[tex]\sqrt[]{5\cdot5}=\sqrt[]{5^2}=\text{ 5}[/tex]________________________
Answer
√25 = 5
I need help with this question but no one is helping me! Can someone please help me
Answer:
Step-by-step explanation:
Number of yellow marbles =13
Number of teal marbles = 13
Two marbles are drawn randomly
Probability that both marbles are teal
Hence the probability that both marbles are teal is 0.026
HI there. I need some help with this question. I cannot figure out what the answer is.
From the question we were given the following:
Area of the square is 19 square units
Area of the circle is 30 square units
Area of intersection is 3 square units.
We are asked to find the area in square units of the entire coloured region.
So,
Are of Square = 19 square units
Are of Circle = 30 square units
Area of Intersection = 3 square units
Area of coloured region = Area of Square + Area of Circle - Area of Intersection
Therefore, Area of coloured region = 19 + 30 - 3
= 46 saqure units.
An arrow is launched upward with a velocity of 320 feet per second from the top of a 30-foot building. What is the maximum height
attained by the arrow?
Answer: Maximum height reached is 804.88 m
Step-by-step explanation:
At maximum height velocity is zero
We have equation of motion v² = u² + 2as
Initial velocity, u = 320 ft/s = 97.536 m/s
Final velocity, v = 0 m/s
Acceleration, a = -9.81 m/s²
Substituting
v² = u² + 2as
0² = 97.536² + 2 x -9.81 x s
s = 484.88 m
So the arrow further a height of 484.88 m
Total height = 320 + 484.88 = 804.88 m
Find the coefficient of third term of (x + 2)³. A. 40 OB. 10 OC. 20 D. 80 Reset Selection A
Given:
The expression given is,
[tex]\left(x+2\right)^5[/tex]Required:
To find the coefficient of the third term.
Explanation:
Let us expand the expression to find the coefficient.
[tex]\begin{gathered} \left(x+2\right)^5 \\ =\frac{5!}{5!}x^52^0+\frac{5!}{4!}x^42^1+\frac{5!}{2!3!}x^32^2+\frac{5!}{3!2!}x^22^3+\frac{5!}{4!1!}x^12^4+\frac{5!}{5!0!}x^02^5 \\ =x^5+10x^4+40x^3+80x^2+80x+32 \end{gathered}[/tex]Hence, the coefficient of the third term is 40.
Final Answer:
The coefficient of the third term is 40.
Option A is correct.
4) The measure of one of two supplementary angles is 8 degrees more than three times the other. Find the measure of the larger of the two angles.
Supplementary angles add 180 degrees.
One of the two angles is 8 degrees more than 3 times the other.
If one of the angles is A and the other is B, then:
[tex]A=8+3B[/tex]As they are supplementary, they add 180 degrees:
[tex]A+B=180[/tex]We replace the information of the second equation in the first one and solve:
[tex]\begin{gathered} A=180-B \\ A=8+3B=180-B \\ 8+3B=180-B \\ 4B+B=180-8 \\ 5B=172 \\ B=\frac{172}{5} \\ B=34.4 \end{gathered}[/tex]Now we can solve for the other angle:
[tex]A=8+3B=8+3(34.4)=8+103.2=111.2[/tex]The measure of the angles is 34.4 degrees and 111.2 degrees.
To the nearest tenth of pound Does has need to buy?
Answer: She needs approximately 142.5 pounds
Explanation:
From the information given,
A pound of fertilizer covers 39 square feet of lawn.
If the lawn measures 5557.4 square feet, then
the number of pounds of fertilizer that she needs to buy = 5557.4/39 = 142.4975
Rounding to the nearest tenth,
She needs approximately 142.5 pounds
Find an angle θ with 0∘<θ<360∘ that has the same:
Sine function value as 210∘
θ = _____ degrees
Cosine function value as 210∘
θ = ______ degrees
sin theta = -0.5 degrees
cos theta=-0.86 degrees
hope it helped
√X²+5x+4/X²+8x+16 - X²-3x-4/X²-16
The expression given as [x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] simplifies to 0
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16]
Factorize the expression
So, we have
[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] = [(x + 4)(x + 1)]/[(x + 4)(x + 4)] - [(x - 4)(x + 1)]/[(x + 4)(x - 4)]
Simplify the common factors
So, we have
[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] = [(x + 1)]/[(x + 4)] - [(x + 1)]/[(x + 4)]
The terms of the above equation are the same
So, the result of subtracting one from the other is 0
This gives
[x²+ 5x + 4]/[x² + 8x + 16] - [x² - 3x - 4]/[x²-16] = 0
Hence, the value of the expression is 0
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The volume for a rectangular prism is given by the formula V = l · w · h, where l is the length of the prism, w is the width of the prism, and h is the height of the prism.
If the volume of a rectangular prism with a height of 8 inches is 200 cubic inches and the base of the prism is a square, then what is the width of the rectangular prism?
A.
5 inches
B.
12.5 inches
C.
25 inches
D.
40 inches
If the volume of a rectangular prism with a height of 8 inches is 200 cubic inches and the base of the prism is a square, then the width of the rectangular prism is 5 inches
The volume of the rectangular prism = 200 cubic inches
The height of the rectangular prism = 8 inches
We know the volume of the rectangular prism = l×w×h
Where ls if the length of the base
w is the width of the base
h is the height of the rectangular prism
Given that the base of the prism is a square, then the length of the base is equal to width of the base
Consider
l = w = x
Substitute the values in the equation of volume
x × x × 8 = 200
[tex]x^{2}[/tex] × 8 = 200
[tex]x^{2}[/tex] = 25
x = 5 inches
Hence, if the volume of a rectangular prism with a height of 8 inches is 200 cubic inches and the base of the prism is a square, then the width of the rectangular prism is 5 inches
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Round to the answer to the nearest tenth.18. A 24-foot ladder leaning against a building forms an 18° angle with the side of the building,How far is the base of the ladder from the base of the building?
In order to solve this problem, first let's draw the corresponding image to the problem:
Then, to calculate the distance x, we can use the sine relation of the angle of 18°.
The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \sin (18\degree)=\frac{x}{24} \\ \text{0}.309=\frac{x}{24} \\ x=24\cdot0.309 \\ x=7.42 \end{gathered}[/tex]So the distance wanted is 7.42 ft.
Marsha thinks that because 123 is greater than 68, 0.123 must be greater than 0.68. Show and explain why Marsha is incorrect.
Let's begin by listing out the information given to us:
[tex]\begin{gathered} 123=1\text{0}0 \\ \text{ 20} \\ \text{ 3} \\ 123=1\text{ hundred + 2 tens + 3 units} \\ 68\text{ = 6 (10)} \\ \text{ 8} \\ 68\text{ = 6 tens + 8 units} \end{gathered}[/tex]To know which is greater between 0.123 To know which i3& 0.68, let's express it in tenth, hundredth & thousandth
[tex]\begin{gathered} 0.123=3\text{ thousandth + 2 hundredth + 1 tenth + 0 unit} \\ 0.123=0.003+0.02+0.1+0 \\ 0.68=\text{ 6 hundredth + 8 tenth + 0 unit} \\ 0.68=0.60+0.08+0 \end{gathered}[/tex]0.123 has 3 decimal places, which means it is 123/1000
0.68 has 2 decimal places, which means it is 68/100
When you multiply by 100, we have:
0.123 * 100 = 12.3
0.68 * 100 = 68
It becomes very evident that 0.68 is greater than 0.123
Find solutions to the linear equation y=12x+24
Te solutions to the linear equation given as y = 12x + 24 are (0, 24), (1, 36) and (2, 48)
How to determine the solutions to the linear equation?From the question, the linear equation is given as
y = 12x + 24
To determine the solutions, we assume values for the variable x and then calculate the y values
Having said that, we have
y = 12x + 24
Set x = 0
So, we have
y = 12 x 0 + 24 = 24
Set x = 1
So, we have
y = 12 x 1 + 24 = 36
Set x = 2
So, we have
y = 12 x 2 + 24 = 48
So, the ordered pairs of the solutions are (0, 24), (1, 36) and (2, 48)
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Simplify the expression √(112x^10 y^13 ). Show your work. please help
To create the abbreviated expression, combine similar terms by adding them all together. If the expression be [tex]$\sqrt{112 x^{10} y^{13}}$[/tex] then expression exists [tex]$4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex].
What is meant by an expression?Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.
Start by recognizing the like terms, or terms with the same variables and exponents, in algebraic formulas. Then, to create the abbreviated expression, combine similar terms by adding them all together.
Let the expression be [tex]$\sqrt{112 x^{10} y^{13}}$[/tex]
separating the roots of the expression, we get
[tex]$\sqrt{112 x^{10} y^{13}}=\sqrt{112} \sqrt{x^{10}} \sqrt{y^{13}}$[/tex]
simplifying the above equation, we get
[tex]$=\sqrt{112} \sqrt{x^{10}} \sqrt{y^{13}}$[/tex]
Simplify [tex]$\sqrt{x^{10}}= x^5$[/tex]
[tex]$=\sqrt{112} x^5 \sqrt{y^{13}}$[/tex]
Simplify [tex]$\sqrt{y^{13}}=y^6 \sqrt{y}$[/tex]
[tex]$=\sqrt{112} x^5 y^6 \sqrt{y}$[/tex]
[tex]$=\sqrt{112}=4 \sqrt{7}$[/tex]
[tex]$=4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex]
Therefore, the correct answer is [tex]$4 \sqrt{7} x^5 y^6 \sqrt{y}$[/tex].
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Starting at sea level, a submarine descended at a constant rate to a depth of −34 mile relative to sea level in 5 minutes.
What was the submarine's depth relative to sea level after the first minute?
Enter your answer as a fraction in simplest form.
Based on the fact that the submarine's depth was descended to at a constant rate, the submarine's depth relative to sea level with the passing of the first minute was -6⁴/₅ miles
How to find the submarine depth?The submarine descended at a constant rate to the current depth of -34 miles in 5 minutes. This means that the rate can be found by the formula:
= Current depth / Time
= -34 / 5
= -6.8 miles per minute
After the first minute, the depth is:
= -6.8 x 1
= -6.8 miles
This number in fractions is:
= -6 + 8/10
= -6 + 4 / 5
= -6⁴/₅ miles
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Help Please!
A.
[tex] \frac{3}{4} [/tex]
B.
[tex] \frac{5}{4} [/tex]
C.
[tex] \frac{3}{5} [/tex]
D.
[tex] \frac{4}{5} [/tex]
Answer:
Step-by-step explanation:
Soh Cah Toa
S stand for sine, C stand for Cosine and the T stand for Tangent
'o' is the opposite, 'a' stand for adjacent (next to) and h stand for hypotenuse (the longest length of the triangle)
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
We care about angle A and we want sine. So we will use the first equation.
The opposite from A is 3 and the hypotenuse is 5.
[tex]sin(A)=\frac{3}{5}[/tex]
What’s 2,0000000 +3000,00000
In order to add these two numbers, we need to add the algarisms that are in the same position.
Since the first number has 7 zeros and the second one has 8 zeros, the numbers 2 and 3 will not be added, since they are in different positions (the number 3 has more "value", since it's in a higher position).
So, adding these two numbers, we have:
Therefore the result of this sum is 320,000,000 (three hundred and twenty million).
will give brainlist
Solve the inequality n minus three fifths is less than or equal to negative four sevenths for n.
n is greater than or equal to negative forty one over thirty five
n is less than or equal to negative one over thirty five
n is less than or equal to one over thirty five
n is greater than or equal to forty one over thirty five
The solution to the given inequality would be n ≤ 1/35 which is the correct answer would be an option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We have to determine the solution of the inequality n minus three-fifths is less than or equal to negative four sevenths for n.
As per the given condition, translate the phrase into an algebraic inequality as :
⇒ n - 3/5 ≤ - (4/7)
⇒ n ≤ 3/5 - (4/7)
⇒ n ≤ (21 - 20)/35
⇒ n ≤ 1/35
Therefore, the solution to the given inequality would be n ≤ 1/35.
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Given H(t)=10-2t^2 , find h^-1 (t), is h (t) one to one ? What does this imply about h^-1(t)
We have the function:
[tex]H(t)=10-5t^2[/tex]And we have to find the inverse function.
We can write this as:
[tex]H(H^{-1}(t))=t[/tex]We can solve this as:
[tex]\begin{gathered} H(H^{-1}(t))=10-2(H^{-1})^3=t \\ 10-2(H^{-1})^3=t \\ 2(H^{-1})^3=10-t \\ (H^{-1})^3=\frac{10-t}{2} \\ H^{-1}=\sqrt[3]{\frac{10-t}{2}}^{} \end{gathered}[/tex]The inverse function is:
[tex]H^{-1}=\sqrt[3]{\frac{10-t}{2}}^{}[/tex]The domain of H is all the real numbers, as the domain of H^-1.
Ava can run 4/5 of a mile in 4/3 of an hour. How far can she run in 1 hour? *
Answer:
She can run 3/5 miles in 1 hour
Explanation:
Given that Ava can run 4/5 of a mile in 4/3 of an hour, we want to find how far she can run in 1 hour.
Let x represent the number of miles she can run in one hour.
The statement can be represented in the pair of equations:
[tex]\begin{gathered} \frac{4}{5}miles=\frac{4}{3}\text{hours} \\ \\ x\text{ hour }=1\text{hour} \end{gathered}[/tex]Using these equations, we have:
[tex]\begin{gathered} \frac{4}{5}=\frac{4}{3}x \\ \\ x=\frac{\frac{4}{5}}{\frac{4}{3}} \\ \\ x=\frac{4}{5}\times\frac{3}{4} \\ \\ =\frac{3}{5} \end{gathered}[/tex]That is, she can run 3/5 miles in 1 hour
In a triple batch of a spice mix, there are 6 teaspoons of garlic powder and 15
teaspoons of salt. Answer the following questions about the mix.
2. How much salt is used with 8 teaspoons of garlic powder
3. If there are 14 teaspoons of spice mix, how much salt is in it.
4. How much More salt is there than garlic powder if 6 teaspoons of garlic powder are use
The answers of the given questions are:
8 teaspoons of garlic powder are combined with 20 tablespoons of salt.10 teaspoons of salt are included in every 14 teaspoons of spice mixture.If 6 teaspoons of garlic powder are used, there are 15 teaspoons more salt than garlic powder.What exactly are ratio and proportion?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as: 1: 3 (for every one boy, there are three girls).Given: There are 6 teaspoons of garlic powder and 15 teaspoons of salt in a triple batch of spice mix.
Let x be the teaspoons of salt.
Salt used with 8 teaspoons of garlic powder:
6/15 = 8/x
x = 20
Therefore, 20 teaspoons of salt is used with 8 teaspoons of garlic powder.
6 + 15 = 21 teaspoons of spice mix
Salt used in 14 teaspoons of spice mix:
21/15 = 14/x
x = 10 teaspoons of salt.
Therefore, if there are 14 teaspoons of spice mix, 10 teaspoons of salt is there in it.
If 6 teaspoons of garlic powder are used then,
21-6 = 15 teaspoons of more salt is used
Therefore, 15 teaspoons of more salt is there than garlic powder if 6 teaspoons of garlic powder are used.
The answers of the given questions are:
20 teaspoons of salt is used with 8 teaspoons of garlic powder.If there are 14 teaspoons of spice mix, 10 teaspoons of salt is there in it. 15 teaspoons of more salt is there than garlic powder if 6 teaspoons of garlic powder are used.Learn more about ratio and proportion here:
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According to the Oxnard College Student Success Committee report in the previous year, we believe that 22% of students struggle in their classes because they don't spend more than 8 hours studying independently outside of a 4-unit class. For this year, you would like to obtain a new sample to estimate the proportiton of all Oxnard students who struggle in their classes because they don't study enough outside of the classrooms. You would like to be 95% confident that your estimate is within 1.5% of the true population proportion. How large of a sample size is required? Do not round mid-calculation.n =
The required sample size, using the z-distribution, is given as follows:
n = 253.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The equation for the margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 95%, hence the critical value z has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate and the margin of error are given as follows:
[tex]\pi = 0.22, M = 0.015[/tex]
Hence the required sample size is calculated as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.015 = 1.96\sqrt{\frac{0.015(0.985)}{n}}[/tex]
[tex]0.015\sqrt{n} = 1.96\sqrt{0.015(0.985)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.015(0.985)}}{0.015}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.015(0.985)}}{0.015}\right)^2[/tex]
n = 253. (rounding up, as a sample size of 252 would result in a margin of error slightly above 1.5%).
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Write the standard form equation of an ellipse with foci(-3,1)and(-3,13) and eccentricity e=0.6.
Given:
[tex]\begin{gathered} foci:-3,1),and,(-3,13) \\ And,eccentricity,e=0.6 \end{gathered}[/tex]To Determine: The standard form equation of an ellipse
Solution
The half life of radium -226 is 1640 years. If a sample contains 200 mg, how many mg will remain after 4000 years?