Answer:
-3/2
Step-by-step explanation:
multiply both sides by y:
y-6 = 5y
subtract y from both sides:
-6 = 4y
divide both sides by 4:
-6/4 = y
y = -3/2
Answer:
[tex]\frac{y-6}{y}=5\quad :\quad y=-\frac{3}{2}[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}y\\\frac{y-6}{y}y=5y\\\mathrm{Simplify\:}\frac{y-6}{y}y:\quad y-6\\y-6=5y\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}\\y-6+6=5y+6\\y=5y+6\\\mathrm{Subtract\:}5y\mathrm{\:from\:both\:sides}\\y-5y=5y+6-5y\\-4y=6\\\mathrm{Divide\:both\:sides\:by\:}-4\\\frac{-4y}{-4}=\frac{6}{-4}\\y=-\frac{3}{2}[/tex]
OR
[tex]y-\frac{6}{y}=5\quad :\quad y=6,\:y=-1[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}y\\yy-\frac{6}{y}y=5y\\y^2-6=5y\\\mathrm{Solve\:}\:y^2-6=5y:\quad y=6,\:y=-1[/tex]
Hope this helps!!!!
express with positive exponents
Answer:
2b^2
--------------
5a^4
Step-by-step explanation:
2a^-4
-------------
5b^-2
Negative exponents go to the denominator when they are in the numerator
and to the numerator when they are in the denominator
a^-4 becomes 1/a^4
1/b^-2 becomes b^2
2/5 * 1/a^4 * b^2
2*b^2 * 1/5a^4
Rewriting
2b^2
--------------
5a^4
Six men completed a task in 24 hrs and 48 min. How long, in hours and minutes, would it take four men to complete the same task?
Answer:
It would take 4 men 37 hrs and 12 mins to complete the same task.
step-by-step explanation:
Let X be the time the four men would use to complete the task.
From the question, 6 men completed a task in 24 hrs and 48 mins
But
[tex]24 \: hrs \: 48 \: mins = 24(60mins) + 48 \: mins=1488 \: mins[/tex]
Using ratio and proportion
[tex]6 \: men:1488 \: mins[/tex]
[tex]4 men:x\:mins[/tex]
if more, less divides and if less, more divides.
4 men required more time to complete the task
Hence:
[tex]x = \frac{6}{4} \times 1488 \: mins[/tex]
[tex]x = 2232 \: mins[/tex]
x = 37 hrs 12 mins
Solve the inequality. Graph the solution . -1.6 < m/-2.5
Required sοlutiοn of inequality οf -1.6 < m/-2.5 is m < 4
Here given,
We can begin by multiplying bοth sides οf the inequality by -2.5:
[tex]$-1.6\lt \sm < {\frac{m}{-2.5}}$[/tex]
Sο the sοlutiοn tο the inequality is m < 4.
[tex]$\begin{array}{l}{{\rm -1.6 < \dfrac{m}{-2.5}}}\\\\ {{\rm -1.6\times\left(-2.5\right) \gt > m}}\\\\ {{\rm 4\gt > m}}\end{array}$[/tex]
Tο graph this sοlutiοn, we can plοt a number line with an οpen circle at 4, since m is nοt equal tο 4. Then we shade the part οf the number line tο the left οf 4, indicating all values οf m that satisfy the inequality.
The graph shοws that all values οf m tο the left οf 4, including 4 itself, satisfy the inequality.
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To solve the inequality -1.6 < m/-2.5, we multiply both sides by -2.5 and reverse the inequality sign, resulting in m being less than 4. This solution can be graphed on a number line with an open circle at 4 and shading to the left.
Explanation:To solve the inequality -1.6 < m/-2.5, we need to manipulate the inequality to isolate the variable m.
First, multiply both sides of the inequality by -2.5 to get m by itself. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. So:
The inequality now reads as m is less than 4.To graph this solution, draw a number line and make an open circle at 4, indicating that 4 is not included in the solution. Then, shade everything to the left of 4 to represent all the numbers that are less than 4.
Divide $414 into three parts such that first one is two-third of the second and the ratio between second and third is 5 : 7.
Answer:
$90, $135, $189
Step-by-step explanation:
Since the first part of the ratio is two- thirds of the second, then
first part = [tex]\frac{2}{3}[/tex] × 5 = [tex]\frac{10}{3}[/tex]
The ratio is then
[tex]\frac{10}{3}[/tex] : 5 : 7
Sum the 3 parts of the ratio
[tex]\frac{10}{3}[/tex] + 5 + 7 = [tex]\frac{46}{3}[/tex]
Divide the amount to be shared by the sum to find the value of one part of the ratio.
$414 × [tex]\frac{3}{46}[/tex] = $27 ← value of 1 part of the ratio, then
[tex]\frac{10}{3}[/tex] × $27 = $90
5 × $27 = $135
7 × $27 = $189
The 3 parts are $90, $135, $189
1 3/5(t-6)=-0.4 solve the equation
To solve the equation 1 3/5(t-6)=-0.4, first distribute 1 3/5 to the terms inside the parentheses. Then, multiply both sides of the equation by the reciprocal of 8/5 to isolate the variable t. Finally, simplify the equation to find the solution t = 5.75.
Explanation:To solve the equation 1 3/5(t-6)=-0.4, we can follow these steps:
Distribute 1 3/5 to the terms inside the parentheses. This gives us 8/5(t-6)=-0.4.Multiply both sides of the equation by the reciprocal of 8/5, which is 5/8, to cancel out the coefficient on the variable. This gives us t-6 = -0.4 * 5/8.Simplify the equation by multiplying and dividing as necessary. This gives us t-6 = -0.25.Add 6 to both sides of the equation to isolate the variable t. This gives us t = -0.25 + 6.Simplify the equation to find the final solution. This gives us t = 5.75.Therefore, the solution to the equation is t = 5.75.
Final answer:
To solve the equation 1 3/5(t-6)=-0.4, distribute the 1 3/5 first and then simplify the equation by adding and subtracting terms to isolate t. The final solution is t = 2.
Explanation:
To solve the equation 1 3/5(t-6)=-0.4, we can begin by distributing the 1 3/5 to the terms inside the parentheses:
1 3/5(t-6) = 1 3/5 * t - 1 3/5 * 6 = 8/5t - 18/5
Now, we can rewrite the equation as:
8/5t - 18/5 = -0.4
Next, we can get rid of the fraction by multiplying both sides of the equation by 5:
5(8/5t - 18/5) = 5(-0.4)
After simplifying, we get:
8t - 18 = -2
Now, add 18 to both sides of the equation:
8t - 18 + 18 = -2 + 18
Simplifying further, we have:
8t = 16
Finally, divide both sides of the equation by 8 to solve for t:
t = 16/8
Therefore, the solution to the equation is t = 2.
Reduce to simplest form. -3/5 + 1/3=
Answer:
-4/15 (Fraction form) -0.26... (Decimal form)
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
when you add the numerators which are, -3 and 1, you'd end up with -2.
when you add the denominators which are, 5 and 1, you'd end up with 6.
so that would give you -2/6.
when you simplify that you end up with -1/3.
Sixty-two desks can be assembled in 108.5 hours. At this rate, about how many desks can be assembled in 250 hours? Round to the nearest whole number.
Answer:
143 desks
62 desks
108.5 hours
=
x desks
250 hours
15500 = 108.5x
142.8 = x
Round to 143
Step-by-step explanation:
Answer:
In 250 hours 143 seats can be assembled.
Step-by-step explanation:
62 desks can be assembled in 108.5 hours.
In 108.5 hours 62 desks can be assembled.
In 1 hour [tex]\dfrac{62}{108.5}[/tex] seats can be assembled.
In 250 hours [tex]\dfrac{62}{108.5}\times 250[/tex] seats can be assembled.
In 250 hours 142.86 seats can be assembled.
Hence, In 250 hours 143 seats can be assembled. (Round to nearest whole number)
Evaluate the expressions for x=6 3x +5= ? X^3-10=?
Answer:
x^3-10 is greater
Step-by-step explanation:
3(6)+5=18+5=23
6^3-10=206
206>23
Which reason for step 4 completes the proof?
Prove: -(a + b) + a = -b
Answer:
Identity Property of Addition.
Answer:
Reason which completes the proof of step 4 is:
Identity property of addition
Step-by-step explanation:
-(a+b)+a= -b
= -a+ (-b)+a (distributive property)
= -a+a+(-b) (Commutative property of Addition)
= 0+ (-b) (Additive inverse property)
= -b (Identity property of addition)
(Identity property of addition says that if 0 is the identity element and a is any element
Then, a+0=0+a=a)
So, reason which completes the proof of step 4 is:
Identity property of addition
Anyone know the answer? Much appreciate the help!!
Answer:
[tex]x=3+\frac{\sqrt{4L^{2}+1}}{L}[/tex] and [tex]x=3-\frac{\sqrt{4L^{2}+1}}{L}[/tex]
Step-by-step explanation:
we have
[tex]L=\frac{1} {\sqrt{x^2-6x + 5}}[/tex]
Solve for x
That means-----> isolate the variable x
squared both sides
[tex]L^{2} =(\frac{1} {\sqrt{x^2-6x + 5}})^{2}\\ \\L^{2}=\frac{1} {{x^2-6x + 5}}\\ \\x^2-6x + 5=\frac{1}{L^{2}}\\ \\x^2-6x=\frac{1}{L^{2}}-5\\ \\x^2-6x+9=\frac{1}{L^{2}}-5 +9\\ \\x^2-6x+9=\frac{1}{L^{2}}+4\\ \\(x-3)^2=\frac{4L^{2}+1}{L^{2}}[/tex]
Take the square root both sides
[tex](x-3)=(+/-)\sqrt{\frac{4L^{2}+1}{L^{2}}}\\ \\x=3(+/-)\frac{\sqrt{4L^{2}+1}}{L} [/tex]
therefore
[tex]x=3+\frac{\sqrt{4L^{2}+1}}{L}[/tex]
[tex]x=3-\frac{\sqrt{4L^{2}+1}}{L}[/tex]
Please help and thank you
Answer:
(3, 2)
Step-by-step explanation:
Given a graphical representation of a system of equation then the solution is at the point of intersection of the 2 lines, that is
solution is ( 3, 2)
7, 9, 11, 13...
Generalize the pattern by finding an explicit formula for the nth term.
Answer:
an = 5 + 2n
Step-by-step explanation:
Each time it increases by the same amount (2), so this is an arithmetic sequence:
an = a₁ + d (n - 1)
Given a₁ = 7 and d = 2:
an = 7 + 2 (n - 1)
an = 7 + 2n - 2
an = 5 + 2n
Check our answer:
n=1: a₁ = 5 + 2(1) = 7
n=2: a₂ = 5 + 2(2) = 9
n=3: a₃ = 5 + 2(3) = 11
n=4: a₄ = 5 + 2(4) = 13
The pattern represents the arithmetic progression and the explicit formula for the nth term is a(n) = 2n + 5
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have a sequence:
7, 9, 11, 13…
The above pattern represents the arithmetic progression.
The first term a = 7
Common difference d = 2
nth term:
a(n) = 7 + (n - 1)(2)
a(n) = 2n + 5
Thus, the pattern represents the arithmetic progression and the explicit formula for the nth term is a(n) = 2n + 5
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67,124 x = ________. Will the product of this equation be less than or greater than 67,124? Explain your reasoning.
The product could be either less than or greater than 67,124.
If you multiplied by a negative number, you would get a negative number, which is less than a positive number such as 67,124.
If you multiplied by zero, you would get zero, which is less than a positive number such as 67,124.
If you multiplied by one, you would get 67,124, which is equal to 67,124 since they are the same number.
If you multiplied by a positive number less than one, you would get a positive number greater than zero and less than 67,124.
If you multiplied by a positive number greater than one, you would get a positive number greater than 67,124.
A logarithmic function is an appropriate model because, for evenly spaced y-values, the ___ of consecutive x-values is constant.
Answer:
Ratio.
Step-by-step explanation:
A logarithmic function is an appropriate model because, for evenly spaced y-values, the ratio of consecutive x-values is constant. This is the correct answer to your question.
Hope this helps!!!
Kyle.
Answer:
Step-by-step explanation:
Whenever a function is logarithmic function, we get for evenly spaced y,
say y = log x
y+d = log x1
y+2d = log x2
We get
d = [tex]log \frac{x_1}{x} =log \frac{x_2}{x_1}[/tex]
In other words we get the ratios of consecutive x values is constant equal to the difference in consecutive y's.
Graphs, please help. Thank you!
Answer:
B. [tex]F(x)=(x+2)^4[/tex]
Step-by-step explanation:
The parent function is [tex]G(x)=x^4[/tex]
The given translation is of the form;
This shifts the graph of [tex]G(x+k)[/tex] [tex]G(x)=x^4[/tex], k units to the left.
If this function is shifted 2 units to the left, its equation will now be
[tex]F(x)=(x+2)^4[/tex]
The correct choice is B. [tex]F(x)=(x+2)^4[/tex]
The city council is planning to construct a park on North Street that has a triangular perimeter. They want to place a fountain at a point equidistant from all three sides of the park. Where should the council place the fountain?
A.
at the point of intersection of the angle bisectors and perpendicular bisectors of the park
B.
at the center of the inscribed circle of the park
C.
at the center of the circumscribed circle of the park
D.
at the point of intersection of the lines perpendicular to two sides of the park
E.
at the point of intersection of the medians of the park
B.
At the center of the inscribed circle of the park
Answer:
B
Step-by-step explanation:
that would be B. This circle touches each side of the triangle and has a center which is equidistant from all of the sides.
22n=418
what is the vaule of n.
Answer:
n = 19
Step-by-step explanation:
22n = 418
Divide both sides by 22.
n = 19
What are the solutions of the equation 3x^2+8x=12
x= -4/3 + 2/3 square root of 13 or x= -4/3 + -2/3 square root of 13 !!
Answer:
Step-by-step explanation:
3x² + 8x = 12
3x² + 8x - 12 = 0
a=3, b=8, and c=-12. Solving with quadratic formula:
x = [ -b ± √(b² - 4ac) ] / 2a
x = [ -8 ± √(8² - 4(3)(-12)) ] / 2(3)
x = (-8 ± √208) / 6
x = (-8 ± 4√13) / 6
x = -4/3 ± 2/3 √13
If a normal distribution has a mean of 44 and a standard deviation of 8, what is the zscore for a value of 50
Answer:
0.75
Step-by-step explanation:
Z-score tells the no. of standard deviations a data point is from the mean.
the formula for z score is given by
z-score= (data value - mean) / standard deviation
Given:
mean=44
standard deviation= 8
data point=50
putting the values of mean(44), standard deviation(8) and given data value(50) in the above equation
z-score= (50-44)/8
= 6/8
=0.75 !
there are four colors red white black and blue on a spinner and there is a coin . what is the probability of spinning a red and heads?
Answer: 1/8
Step-by-step explanation: There is 1/4 of a chance of spinning a red, and 1/2 of a chance of getting a heads. Multiply these numbers.
1/4 x 1/2 = 1/8
There is a 1/8 chance of this outcome.
The eggs of birds and other animals come in many different shapes and sizes. Eggs often have a shape that is nearly spherical. When this is true, you can use the formula for a sphere to find their volume.
The green turtle lays eggs that are approximately spherical with an average diameter of 4.1 centimeters. Each turtle lays an average of 113 eggs at one time. Find the volume of one egg, rounding your answer to the nearest tenth of a cubic centimeter. Then find the total volume of these eggs, to the nearest tenth of a cubic centimeter
The eggs are approximately 2.1 and which each turtle does not lay 113 they lay 123 eggs each year around which you subtract it all up and it comes out to 120.9.then the you divide all up which gives you your answer to your problem.
Final answer:
The volume of one spherical green turtle egg with a diameter of 4.1 cm is approximately 36.2 cubic centimeters. The total volume of 113 such eggs is about 4091.6 cubic centimeters when rounded to the nearest tenth.
Explanation:
To calculate the volume of one green turtle egg, we use the formula for the volume of a sphere, which is V = 4/3 πr³, where r is the radius of the sphere. Since the egg has a diameter of 4.1 centimeters, the radius is half of that, which is 2.05 centimeters. Plugging this value into the formula gives us V = 4/3 π(2.05 cm)³ ≈ 36.2 cubic centimeters when rounded to the nearest tenth.
Next, we calculate the total volume of eggs laid by one turtle. Since each turtle lays 113 eggs, the total volume is 113 × 36.2 cm³ = 4091.6 cm³, which rounds to 4091.6 cubic centimeters.
Need correct answer ASAP please
Answer:
C = 16pi
Step-by-step explanation:
Since we are evaluating for the circumference, we plug in the r. Since r=8, we get 2*pi*8 or 16pi.
answer should be C gl btw
Choose the solution(s) of the following system of equations:
x2 + y2 = 6
x2 – y = 6
I think this is the answer X = 3 + 1/2y
The solutions for the system of equations are:
[tex]\[ (x, y) = (\sqrt{6}, 0), (-\sqrt{6}, 0), (\sqrt{5}, -1), (-\sqrt{5}, -1) \][/tex]
To solve the system of equations[tex]\(x^2 + y^2 = 6\)[/tex] and [tex]\(x^2 - y = 6\)[/tex], we can use substitution or elimination method. Let's solve it using the substitution method:
Given equations:
1.[tex]\(x^2 + y^2 = 6\)[/tex]
2.[tex]\(x^2 - y = 6\)[/tex]
From equation 2, we can express [tex]\(x^2\) as \(y + 6\):[/tex]
[tex]\[x^2 = y + 6\][/tex]
Now, substitute [tex]\(x^2 = y + 6\)[/tex] into equation 1:
[tex]\[y + 6 + y^2 = 6\][/tex]
Rearrange this equation:
[tex]\[y^2 + y + 6 = 6\][/tex]
Subtract 6 from both sides:
\[y^2 + y = 0\][tex]\[y^2 + y + 6 = 6\][/tex]
Factor out y:
[tex]\[y(y + 1) = 0\][/tex]
So, either [tex]\(y = 0\)[/tex] or [tex]\(y + 1 = 0\)[/tex] , which means[tex]\(y = 0\)[/tex] or [tex]\(y = -1\).[/tex]
Now, substitute these values of y back into equation 2 to find the corresponding values of x.
For [tex]\(y = 0\):[/tex]
[tex]\[x^2 - 0 = 6\][/tex]
[tex]\[x^2 = 6\][/tex]
[tex]\[x = \pm \sqrt{6}\][/tex]
For [tex]\(y = -1\):[/tex]
[tex]\[x^2 - (-1) = 6\][/tex]
[tex]\[x^2 + 1 = 6\][/tex]
[tex]\[x^2 = 5\][/tex]
[tex]\[x^2 = 5\][/tex]
So, the solutions for the system of equations are:
[tex]\[ (x, y) = (\sqrt{6}, 0), (-\sqrt{6}, 0), (\sqrt{5}, -1), (-\sqrt{5}, -1) \][/tex]
The system has four solutions: [tex]\((\sqrt{6}, 0)\), \((- \sqrt{6}, 0)\), \((\sqrt{5}, -1)\), and \((- \sqrt{5}, -1)\).[/tex]
Complete question:
Choose the solution(s) of the following system of equations:
x2 + y2 = 6
x2 – y = 6
How many 1/3 -cup servings are in 4 cups
There is 12 1/3-cups in 4 cups
To determine how many 1/3-cup servings are in 4 cups, you divide 4 cups by 1/3 cup per serving, resulting in 12 servings of 1/3 cup each.
Explanation:The question asks how many 1/3-cup servings are in 4 cups. To find the answer, we divide the total number of cups by the size of each serving. Here, we have 4 cups total, and we want to know how many 1/3 cup servings that equates to.
To calculate:
4 cups ÷ (1/3 cup/serving) = 4 ÷ (1/3) = 4 × 3 = 12 servings.
Therefore, there are 12 servings of 1/3 cup in 4 cups.
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What is the probability that the student attended the jazz concert given that student is a junior
Answer: C. 0.60
Step-by-step explanation:
From the given table , the number of students are junior : 60
The total number of students = 137
The probability of selecting any junior is given by :-
[tex]\text{P(Junior)}=\dfrac{60}{137}[/tex]
The number of juniors which who attended Jazz = 36
Then , the probability of selecting a students is junior and attends jazz is given by :-
[tex]\text{P(Junior and Jazz)}=\dfrac{36}{137}[/tex]
Now, the conditional probability that the student attended the jazz concert given that student is a junior will be :-
[tex]\text{P(Jazz}|\text{Junior)}=\dfrac{\dfrac{36}{137}}{\dfrac{60}{137}}\\\\\\=\dfrac{6}{10}=0.60[/tex]
Answer: it’s 0.60
(I just took it)
The line plot shows amount of miles students ran in a week. What is the difference in the lowest miles and the highest miles run in a week? A) 1 1/2 B) 1 1/4 C) 1 3/4 D) 3/4
Answer:
C
Step-by-step explanation:
There are 4 lines in between 2 consecutive integers, so each division is:
1/4 = 0.25
As we see from the graph, the highest miles is at the division before 2, which is 1.75
Also, the lowest miles is at 0.
Hence, difference in highest and lowest is 1.75 - 0 = 1.75
In fraction, [tex]1.75=1\frac{3}{4}[/tex]
correct answer C
Over the weekend, Brady and Jack drove to Key West to go scuba diving. Novw they're preparing to go home. Brady needs gas for his jeep, which gets 21 miles per gallon for gas mileage. When he stops at the gas station, he already has 5 gallons of gas in his tank. he buys more gas for $1.40 per gallon
Answer:
(I'm guessing the question is asking how much money Brady needs to pay.)
Step-by-step explanation:
21-5
(the original amount minus the 5 gallons he already has)
= 16.
so Brady needs 16 gallons.
and every gallon is 1.4
so 16 * 1.4
= 22.40
So brady needs 22.40 dollars.
The total cost of 16 gallons of gas is $22.4.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, 21 miles per gallon for gas mileage.
When he stops at the gas station, he already has 5 gallons of gas in his tank.
So, 21-5=16 miles
He buys gas for $1.40 per gallon
Now, total cost = 16×1.40
= $22.4
Therefore, the total cost of gas is $22.4.
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Need help ASAP!!!!!!!
D
Step-by-step explanation:
2/6 is litterally right there cause it has seven lines and tge 0 doesnt count
Select the simplification that accurately explains the following statement.
I NEED HEELP THIS IS A PLATOWEB QUESTION
Answer:
Choice C is correct
Step-by-step explanation:
We use the law of exponents in this problem;
[tex](a^{b})^{2}=a^{b}*a^{b}[/tex]
Therefore,
[tex](9^{\frac{1}{2} })^{2}=9^{\frac{1}{2} }*9^{\frac{1}{2} }[/tex]
Since the base is the same, that is 9, we simply add the exponents 1/2;
[tex]9^{\frac{1}{2}+\frac{1}{2} }[/tex]
one-half plus one-half is equal to unity and any number raised to one is simply equal to the given number;
[tex]9^{1}=9[/tex]
Write all the factors of 35
.
Use commas to separate them.
Factors of 35 :
1, 5, 7, 35
Answer:
1,5
Step-by-step explanation: