Richard = R & Teo = T
Richard & Teo are combined 41 it means R + T = 41
R = 8 + 2T
R + T = 41 #1
R = 8 + 2T #2
replace 2 in 1
8 + 2T + T = 41
8 + 3T = 41
3T = 41 -8 = 33
T = 11
R = 8 + 2*11 = 30
result = richard is 30 & teo is 11 years old.
2 times of Teo is 22
and 8 years older it means + 8
= 30
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.
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]
Find the vertex and the axis of symmetry of the graph of y=-6(x+4)^2 – 3.
Answer:
vertex = (- 4, - 3 ), equation is x = - 4
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = 6(x + 4)² - 3 ← is in vertex form
with (h, k ) = (- 4, 3 ) ← vertex
The equation of the axis of symmetry is a vertical line passing through the vertex, with equation
x = - 4
Someone plz help with e and f I’ll mark as a brainliest
Answer:
e.) 110 = x
f .) 41 = h
Step-by-step explanation:
e
*vertical angles are congruent
78=x-32
+32 +32
110 = x
f
* alternate exterior angles are congruent
126 = 2h + 44
-44 -44
82 = 2h (divide both sides by 2)
41 = h
-10w + 12 = -9w + 13
What value of w makes the equation true?
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]
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.
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
Learn more about the straight line here:
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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
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.
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
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.
At a local pizza shop, large pizzas cost $14.50 and small pizzas cost $9.00. On Thursday, the number of large pizzas sold was 3 less than twice the number of small pizzas sold. The total value of all pizzas sold was $640.50. How many of each type of pizza did the pizza shop sell?
Answer:
Small pizzas = 21
Large pizzas = 39
Step-by-step explanation:
The number of small pizzas sold be x
So, the number of large pizzas sold be 2x - 3
And the total value is $640.504
Now the equation would be
$14.50x + $9 × (2x - 3) = $640.50
$14.50x + 18x - $27 = $640.50
$32.50 = $640.50 + $27
$32.50x = $667.50
x = 21
Now the large pizzas is
= 2 × 21 - 3
= 39
The same is to be considered
Factor [tex] {9}^{2} - 400[/tex]
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
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:
Jeans are on sale for $16 per pair. How much will 4 pairs of jeans cost?
Answer:
4 pairs cost $64
Step-by-step explanation:
16*4=64$
Need help, please!!!
Read question carefully...
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
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.
Can anyone please help me with this?
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
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
Helpppppppppppppppppppppp
At a local fitness center members pay an 8$ membership fee and $3 for each aerobics class nonmembers pay $5 for each aerobics class for what number of aerobics classes will the cost for members and nonmembers be the same
Answer:
4 aerobics classes
Step-by-step explanation:
8 + 3x = 5x
8 = 2x
4 = x
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.
learn more about sequences here :
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Please I need some answers a few is fine
Answer:
a. 9 b.36 c. 100 d. 13689
-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]
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?
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 ______.