Answer:
[tex]\bold{x_1=1\ ,\quad x_2=-\dfrac83}[/tex]
Step-by-step explanation:
[tex]3x^2+5x-8=0\quad\implies\quad a=3\,,\ b=5\,,\ c=-8\\\\x=\dfrac{-5\pm\sqrt{5^2-4(3)(-8)}}{2\cdot3}=\dfrac{-5\pm\sqrt{25+96}}{6}=\dfrac{-5\pm\sqrt{121}}{6}\\\\ x_1=\dfrac{-5+11}{6}=1\ ,\qquad x_2=\dfrac{-5-11}{6}=\dfrac{-16}6=-\dfrac83[/tex]
If a loaf of bread was priced $1.50 on one day and $1.20 the next, what is the percent decrease
of the price of the loaf of bread?
Answer:
20 percent decrease
Step-by-step explanation:
0.15 cents is 10 percent of 1.50, and that multiplied by 2 is 0.30 cents. 0.30 cents is equal to 20 percent, and the difference between 1.50 and 1.20 is 30 cents.
the nth term of a sequence is 3n squared divided by 2 what is the second term of the sequence?
Answer:
6.
Step-by-step explanation:
f(n)=3n²/2
f(2)=3(2²)/2
f(2)=3(4)/2
f(2)=12/2
f(2)=6
The second term of the sequence 3n²/2 is 6.
What is substitution?Substitution in mathematics is when we replace some specific numerical values to variables according to our wants or given in the problem.
Given, The nth term of a sequence is 3n²/2.
Let f(n) = 3n²/2.
Now, to obtain the second term of the sequence can be obtained by replacing n with 2.
∴ f(2) = 3(2)²/2.
f(2) = (3×4)/2.
f(2) = 12/2.
f(2) = 6.
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What is 5.6 x 10 to the 5th power in standard notation ?
A. 0.000056
B. 560,000
C. 5.6 to the 5th power
D. 5,600,000
Answer:
B. 560000
Step-by-step explanation:
You move the decimal over 5 times to the right and there is your answer
You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 201 km south and 194 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?
Answer:
The answer is "0.0846276476".
Step-by-step explanation:
Let all the origin(0,0) of JBLM be
Let the y-axis be north along with the vector j unit.
But along the + ve x-axis is east, and all along with the vector unit i.
And at (194,-201) that undisclosed position is
Mt. Ris (56,-40) at
Let the moment it gets close to the Mt. rainier bet.
Oh, then,
If we know, the parallel to the direction from the point was its nearest one to a path to a point,
Calculating slope:
[tex]\to m=\frac{y_2-y_1}{x_2-x_1}\\[/tex]
points: (0,0) and (194,-201)
[tex]\to m=\frac{-201 -0 }{194-0}\\\\\to m=\frac{-201}{194}\\\\\to m=-1.03[/tex]
equation of the line:
[tex]\to y= mx+c\\\\\to y= -1.03\ x+c[/tex]
when the slope is perpendicular= [tex]-\frac{1}{m}[/tex]
[tex]= - \frac{1}{ -1.03}\\\\= \frac{1}{ 1.03}\\\\= 0.97[/tex]
perpendicular equation:
[tex]\to y-(-40)=0.97 \times (x-56) \\\\\to y+40=0.97 \times (x-56) \\\\[/tex]
Going to solve both of the equations to have the intersection point,
We get to the intersect level in order to be at
(47.16,-48.5748)
so the distance from origin:
[tex]= \sqrt{(47.16^2+48.5748^2)}\\\\= \sqrt{2224.0656 + 2359.5112}\\\\=\sqrt{4583.5768}\\\\=67.7021181[/tex]
[tex]\to time =\frac{distance }{speed}[/tex]
[tex]= \frac{67.7021181}{800}\\\\= 0.0846276476[/tex]
Helpppppppppppppppppppppp
During a lunch period, a survey is done about the students at LCHS with the following results:
1 out of 28 students are wearing a blue t-shirt
1 out of 2 students are girls
1 out of 3 students has a class in C Hall
1 out of 14 students are in band
What are the chances (probability) of randomly selecting a female band member wearing a blue t-shirt who has a class in C hall? Show work.
Answer:
1 in 47.
Step-by-step explanation:
Add all of the outcomes (28 + 2 + 3 + 14).
You'll get 47.
Do not add the 1s.
There is your answer.
1 in 47.
-6x + 3x = -21 solving for variable
x= 7 is the answer
Combine like terms
-3x=21
Divide both sides by 3
x=7
Answer:
[tex]:\implies \sf -6x + 3x = -21 \\ \\ \\ [/tex]
[tex]:\implies \sf - 3x = -21\\ \\ \\ [/tex]
[tex]:\implies \sf x = \dfrac{-21}{ - 3} \\ \\ \\ [/tex]
[tex]:\implies \sf x = \dfrac{21}{3} \\ \\ \\ [/tex]
[tex]:\implies \underline{ \boxed{ \textsf { \textbf{x = 7}}}} \\ [/tex]
What is an equation of the line that passes through the point (1, 6) and is perpendicular to the line x + 3y = 27?
Answer: y=3x+3
Step-by-step explanation:
The equation of the line that passes through the point (1, 6) and is perpendicular to the line x + 3y = 27 is y = 3x + 3
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The point (1, 6) and is perpendicular to the line x + 3y = 27
The slope of the line x + 3y = 27
m = -1/3
The slope of the line perpendicular to the line x + 3y = 27:
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
M = 3
The equation of the line:
y - 6 = 3(x - 1)
y = 3x + 3
Thus, the equation of the line that passes through the point (1, 6) and is perpendicular to the line x + 3y = 27 is y = 3x + 3
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Mr. Harrison spent a total of $3510 on plane tickets for a family vacation. If each plane ticket cost $585, how many plane tickets did Mr. Harrison purchase?
How many solutions does the equation 4x +2(x-5)=3(2x-4) have?
Answer:
no solutions
Step-by-step explanation:
Given
4x + 2(x - 5) = 3(2x - 4) ← distribute parenthesis on both sides
4x + 2x - 10 = 6x - 12
6x - 10 = 6x - 12 ( add 10 to both sides )
6x = 6x - 2 ( subtract 6x from both sides )
0 = - 2 ← not possible
This indicates the equation has no solution
Can anyone please help me with this?
Differentiate the function.
h(x) = e^x^9+In(x)
Answer:
h'(x)= [tex]e^{x^{9}+In(x) } (9x^{8} +\frac{1}{x} )[/tex]
Step-by-step explanation:
h(x)=[tex]e^{x^{9} +In(x)}[/tex]
first, we will use the chain rule
step1: we divide the function into two parts So,
f(x)=[tex]e^{x^{9} +In(x)}[/tex] and g(x)=[tex]x^{9} +In(x)[/tex]
step2: rewrite [tex]x^{9} +In(x)[/tex] as u.
f(x)=[tex]e^{u}[/tex] and g(x)=u
step3: differentiate f(x) first.
f'(x)=[tex]e^{u}[/tex] (the formula is y=[tex]e^{x}[/tex] and y'=[tex]e^{x}[/tex] - the same)
step4: write the value of u for each function but now sub it in the differentiable form of f(x).
f'(x)=[tex]e^{x^{9}+In(x) }[/tex] and g(x)=[tex]x^{9}+In(x)[/tex]
step5: differentiate the function g(x).
g'(x)=[tex]9x^{8} +\frac{1}{x}[/tex]
(for [tex]x^{9}[/tex] the formula is y=[tex]x^{n}[/tex] and y'=[tex]nx^{n-1}[/tex] ) (for In(x) the formula is y=In(x) and y'=[tex]\frac{1}{x}[/tex] )
step6: use the chain rule to finish out So,
h'(x)=f'(x) × g'(x)
=[tex]e^{x^{9}+In(x) }[/tex] × [tex]9x^{8}+\frac{1}{x}[/tex]
step7: simplify.
h'(x)= [tex]e^{x^{9} +In(x)}(9x^{8}+\frac{1}{x})[/tex]
does anyone know this
Answer:
A
Step-by-step explanation:
when you open the brackets you do 5 to the power of 5 and X to the power of 5
a computer shop charges 20 pesos per hour (or a fraction of an hour) for the first two hours and additional 10 pesos per hour for each succeeding hour. find how much you would pay if you used one of their computers for 40 minutes. show solutions.
Answer:
The equation for the price, as a function of time in hours is:
P(x) = 20*x for 0 ≤ x ≤ 2
P(x) = 40 + 10*(x - 2) for 2 ≤ x
Now, we want to evaluate this function in 40 mins.
we know that 1 hour = 60mins.
Then 40 mins = (40/60) hours = 0.67 hours.
Then we input this in our function, and because this is smaller than 2, we use the first piece of our function:
P(0.67) = 20*0.67 = 13.4
So in 40 mins, the charge will be 13.4 pesos.
х+5y = 3
3х - 2y = -8
Car Survey In a survey of 3,200 people who owned a certain type of car, 1,120 said they would buy
that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
Step-by-step explanation:
In the picture lines AB and CD are parallel. Find the measures of ∠ECF.
Answer:
If the other angle measurment is 38° then angle EFC will be 142° ( 180-38= 142°)
Step-by-step explanation:
The sum of the digits of a two digit number is 11 the number got by interchanging the digits is 27 more than the original number. What is this number ?
Let the digit in one's place be y and digit at ten's place be x.
Given:Sum of the digits = 11
⟶ x + y = 11
⟶ x = 11 - y -- equation (1).
And,
The number formed by reversing the digits is 27 more than the original number.
⟶ Reversed number = Original number + 27
reversed number = 10y + x.
⟶ 10y + x = 10x + y + 27
⟶ 10y + x - 10x - y = 27
⟶ 9y - 9x = 27
Substitute the value x from equation (1).
⟶ 9y - 9(11 - y) = 27
⟶ 9y - 99 + 9y = 27
⟶ 18y = 27 + 99
⟶ 18y = 126
⟶ y = 126/18
⟶ y = 7
Substitute the value of y in equation (1).
⟶ x = 11 - 7
⟶ x = 4
The number = 10(4) + 7 = 40 + 7 = 47.
∴ The required two digit number is 47.
I hope it will help you.
Regards.
The ratios 5 : 3 and 10: 6 ARE equivalent ratios. Which ratio is NOT equivalent to BOTH original ratios?
A. 15: 12
B. 30: 18
C. 15: 9
D. 20: 12
Group of answer choices
C
A
B
D
MATH
7TH GRADE
Answer:
A
Step-by-step explanation:
30:18 /6 =5/3
15:9 /3 =5/3
20:12 /2 =5/3
Answer:
free points
Step-by-step explanation:
thanks sis
Rachel earned $ 34 $34dollar sign, 34 in 4 44 hours at her job today. She wants to know how much she could earn ( e ) (e)left parenthesis, e, right parenthesis tomorrow if she works 10 1010 hours at the same hourly rate. How much will Rachel earn in 10 1010 hours? $
Answer:
Rachel earn $85 in 10 hours.
Step-by-step explanation:
Rachel earned $34 in 4 hours at her job today. It means we can find his earning in 1 hour.
1 hour = $(34/4)
= $8.5
He earns $8.5 in an hour.
To find his earning in 10 hours, multiply $8.5 by 10. So,
Earning = $8.5 × 10
= $85
Hence, Rachel earn $85 in 10 hours.
Answer:
85
Step-by-step explanation:
I am right
What percent of 185 is 70?
(please show work)
Answer:
37.84
Step-by-step explanation:
Step 1: We make the assumption that 185 is 100% since it is our output value.
Step 2: We next represent the value we seek with x.
Step 3: From step 1, it follows that 100%=185.
Step 4: In the same vein, x%=70.
Step 5: This gives us a pair of simple equations:
100%=185(1).
x%=70(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left-hand side) of both equations have the same unit (%); we have
100% / x% = 185 / 70
Step 7: Taking the inverse (or reciprocal) of both sides yields
x% / 100% = 70/185
---> = 37.84%
Therefore, 70 is 37.84% of 185.
Adam wants to create an outdoor rectangular kennel. The length will be three feet more than twice the width. Write and use an equation to find the length and width of the kennel if Adam has 54 feet of fencing. Write and solve an equation to solve this problem.
Step-by-step explanation:
l = 3 + 2w
P= 2w t 2l
= 2w+2(3+2w)
=2w+6+4w
=6w+6 = 54
6w=48
w=8
divide 6 both side
l=3+2(8)=3+16=19
answer
width 8feet and length 19 feet
15 points!!!
4x^2 -20x +25≥0
Answer:
x ≥ [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
Given equation:
4x² -20x + 25≥0
To solve for x, we simply factorize the equation;
We should find two numbers whose sum = -20 and product is 100
These two numbers are -10 and -10
So;
4x² - 10x - 10x + 25 ≥ 0
factorize;
2x(2x - 5) - 5(2x - 5) ≥ 0
(2x - 5) (2x - 5) ≥ 0
So;
2x - 5 ≥ 0
2x ≥ 5
x ≥ [tex]\frac{5}{2}[/tex]
Triangle ABC is transformed to form triangle XYZ. If AC = BC and the perimeter of triangle ABC is 37 inches. What are the lengths of the sides of triangle XYZ that would make triangle ABC congruent to triangle XYZ?
Answer: xy=11 in.; yz= 13 in.; xz=13in.
Step-by-step explanation:
i’m pretty sure that’s it
Please I need some answers a few is fine
Answer:
a. 9 b.36 c. 100 d. 13689
I'm doing a worksheet about dividing fractions and I dont understand it. it's asking me to estimate and then write the quotient in simplest form. the problems are 1.) 1/2 ÷ 1/4. 2.) 4/5 ÷ 2/3. 3.) 14/15 ÷ 7. 4.) 8÷ 1/3. 5.) 12/21 ÷ 2/3. 6.) 5/6 ÷ 5/12. 7.) 5/8 ÷ 1/2.
can anyone help me?
1. answer: 2
2. answer: 1 and 1/5
3. answer: 2/15
4. answer: 24
5. answer: 6/7
6. answer: 2
7. answer: 1 and 1/4
Explanation: Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes _________.
For fraction multiplication, multiply the numerators and then multiply the denominators to get ______.
-10w + 12 = -9w + 13
What value of w makes the equation true?
A 34-year-old woman has a maximum heart rate of 175 bpm. She plans an exercise program so that her heart rate will be between 80% and 90% of her maximum heart rate for at least 30 minutes a day, 3 days a week. Calculate the desired range of heart beats per minute for this exercise program
Answer:
The desired range is from 141 bpm to 157 bpm
Step-by-step explanation:
Given that the maximum heart rate = 175 bpm.
She plans an exercise program to reach the desired heart rate which is in the range of 80% and 90% of the maximum heart rate.
So, the lower limit of the desired heart rate = 80% of the maximum heart rate
=\frac{80}{100}\times 175= 140 bpm
and the upper limit of the desired heart rate = 90% of the maximum heart rate
=\frac{90}{100}\times 175= 157.5 bpm
So, mathematically, the desired range is between 140 bpm and 157.5 bpm.
The heart-beats per minute should be a counting number, so, round the upper limit to the lower integral value to be within the range.
Hence, the desired range is from 141 bpm to 157 bpm.
Jeans are on sale for $16 per pair. How much will 4 pairs of jeans cost?
Answer:
4 pairs cost $64
Step-by-step explanation:
16*4=64$
Nicole babysits on the weekends. She charges a flat fee of $10 and then $5 per hour. If she made $40 on Friday night, how many hours did she babysit?
Choose the equation to represent this situation.
Group of answer choices