Let us assume Doreen rate = x miles per hour.
Sue travels 19 miles per hour faster than Doreen.
Therefore,
Rate of Sue = (x+19) miles per hour.
We know time, rate and distance relation as
Time = Distance / rate.
Therefore, time taken by Doreen to travel 42 miles at the rate x miles per hour =
[tex]\frac{42}{x}[/tex].
And time taken by Sue to travel 100 miles at the rate (x+19) miles per hour =
[tex]\frac{100}{(x+19)}[/tex].
Sue takes 3 hours less time than it takes Doreen.
Therefore,
[tex]\frac{42}{x}-\frac{100}{(x+19)}=3[/tex]
We need to solve the equatuion for x now.
[tex]\frac{42}{x}-\frac{100}{\left(x+19\right)}=3[/tex]
[tex]\mathrm{Find\:Least\:Common\:Multiplier\:of\:}x,\:x+19:\quad x\left(x+19\right)[/tex]
[tex]\mathrm{Multiply\:by\:LCM=}x\left(x+19\right)[/tex]
[tex]\frac{42}{x}x\left(x+19\right)-\frac{100}{x+19}x\left(x+19\right)=3x\left(x+19\right)[/tex]
[tex]42\left(x+19\right)-100x=3x\left(x+19\right)[/tex]
[tex]-58x+798=3x^2+57x[/tex]
[tex]3x^2+57x=-58x+798[/tex]
[tex]3x^2+57x-798=-58x+798-798[/tex]
[tex]3x^2+57x-798=-58x[/tex]
[tex]\mathrm{Add\:}58x\mathrm{\:to\:both\:sides}[/tex]
[tex]3x^2+57x-798+58x=-58x+58x[/tex]
[tex]3x^2+115x-798=0[/tex]
[tex]\mathrm{Solve\:with\:the\:quadratic\:formula}[/tex]
[tex]\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-115+\sqrt{115^2-4\cdot \:3\left(-798\right)}}{2\cdot \:3}:\quad 6[/tex]
[tex]x=\frac{-115-\sqrt{115^2-4\cdot \:3\left(-798\right)}}{2\cdot \:3}:\quad -\frac{133}{3}[/tex]
[tex]x=6,\:x=-\frac{133}{3}[/tex]
We can't take rates as negative numbers.
So, the rate of Doreen (x) = 6 miles per hour.
Rate of Sue = x+19 = 6+19 = 25 miles per hour.
Time taken by Doreen @ 6 miles per hour to cover 42 miles = 42/6 = 7 hours.
Time taken by Sue @ the rate 25 miles per hour to cover 100 miles = 100/25 = 4 hours.
Which of the following equations is written in standard form? A. -2X=13 B. 3x+5y=-15 C.
B
the equation of a line in standard form is
Ax + By = C
where A is a positive integer and B, C are integers
3x + 5y = - 15 is in standard form → B
Answer:
Equation of line in Standard form is
[tex]ax \pm by \pm c=0,[/tex]
Among the two options given,
A. -2 x = 13
Here, coefficient of x= -2
Coefficient of y=0
But we can say that this is a point in one dimensional form.
So, it is not equation of line in standard form.
B. 3 x +5 y= -15
3 x + 5 y +15=0
Comparing with, a x + b y + c=0
a=3, b=5, c=15
Neither the coefficient of x ,nor the coefficient of y is equal to 0.
So, Option B: 3 x + 5 y = -15 →3 x+ 5 y+15=0
is equation of line in standard form.
Correct reason why (x+y)^2 is not equal to x^2+y^2
[tex](x+y)^2 =x^2+2xy+y^2\not=x^2+y^2[/tex]
Help please 19 thru 23
30 POINTS
Which pair of complex numbers has a real-number product? (1 + 2i)(8i) (1 + 2i)(2 – 5i) (1 + 2i)(1 – 2i) (1 + 2i)(4i)
calculating each of the products
noting that i² = (√- 1 )² = - 1
(1 + 2i)(8i) ( distribute by 8i )
= 8i + 16i² = - 16 + 8i ← complex number
(1 + 2i)(2 - 5i) ( expand using FOIL )
= 2 - 5i + 4i - 10i²
= 2 - i + 10 = 12 - i ← complex number
(1 + 2i)(1 - 2i) ( expand using FOIL )
= 1 - 2i + 2i - 4i²
= 1 + 4 = 5 ← real number
(1 + 2i)(4i) ( distribute by 4i )
= 4i +8i² = - 8 + 4i ← complex number
(1 + 2i)(1 - 2i) is the only product which results in a real number
Are the two triangles below similar?
a. Yes; they have congruent corresponding angles.
b. Yes; they have proportional corresponding sides.
c. No; they do not have proportional corresponding sides.
d. No; they do not have congruent corresponding angles.
Answer:
d
Step-by-step explanation:
X(x+3)(x-5)=0 is a quadratic equation
True
False?
False. That is a cubic equation.
The surface area, A, of a sphere in terms of its radius, r, is given by A(r) = 4πr2. Express r as a function of A.
r =√ ( A / 4π )
given A = 4πr² ( isolate r² by dividing both sides by 4π )
A / 4π = r² ( take the square root of both sides )
r =√( A / 4π )
Answer:
The expression of r in terms of A is:
[tex]r=\sqrt{\dfrac{A}{4\pi}}[/tex]
Step-by-step explanation:
We are given the surface area, A, of a sphere in terms of its radius, r, as:
A(r) = 4πr²
[tex]A=4\pi\ r^2[/tex]
⇒ [tex]r^2=\dfrac{A}{4\pi}[/tex]
⇒ [tex]r=\sqrt{\dfrac{A}{4\pi}}[/tex]
Hence, the expression of r in terms of A is:
[tex]r=\sqrt{\dfrac{A}{4\pi}}[/tex]
Without dividing , how can you decide whether the quotient 7.16 ÷ 4 will be less than or greater than 2 ?
Answer and Step-by-step explanation:
Without dividing, I can decide whether the quotient (the number obtained after dividing one number—the numerator—by another—the denominator) of 7.16 ÷ 4 is either less than or greater than 2, by multiplying the denominator (which is 4) by 2, getting the product/result, and comparing the numerator (which is 7.16) with it:
I know that the product of 4 and 2 is 8; however, when comparing 7.16 with 8, I know that it is less than 8; thus I can quickly decide that the quotient of 7.16 ÷ 4 will be less than 2.
A small Company had a profit of -$528 in January if you can use to have the same properties of each month for four months what will the companies total profit be for 4 mont Company had -$528 in January if we can use to have the same profit each month for four months what will the companies total profit months
2112 because i did 528x4=2112
The company's total profit for four months considering it maintains a consistent monthly profit (loss) of -$528 would equate to -$2112.
Explanation:If a company had a profit of -$528 in January and continues to have the same profit for four months, you simply multiply -$528 by four.
To calculate:
Identify the monthly profit: Here, the monthly profit is -$528. This is a loss as it's a negative value. Multiply the monthly profit by the number of months: In this case, it's 4 months. So the calculation will be -$528 * 4 which results in -$2112.
So, the total profit (or in this case, loss) of the company after 4 months will be -$2112.
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Which graph represents the solution set of the system of inequalities?
Y>-2x-2
Y
the graph on the top right
the broken line is the graph of y = - 2x - 2
the slope m = - 2 indicating the graph slopes down from left to right and crosses the y - axis at (0, - 2)
the shaded region above and to the right of the broken line indicates that y is greater than - 2x - 2
top right represents y > - 2x - 2
Q # 13Below are the graphs of. y= |X| - 9
The first graph represents the function y=|x| and the second graph represents the function y=|x|-9.
As you can see they have the same shape.
The x-intercepts of the first and second graphs can be obtained substituting y=0, then:1st graph -
[tex]0=|x|,\\x=0.[/tex]
2nd graph -
[tex]0=|x|-9,\\ |x|=9,\\x=\pm 9.[/tex]
The y-intercept can be obtained substituting x=0, then1st graph -
[tex]y=|0|,\\y=0.[/tex]
2nd graph -
[tex]y=|0|-9,\\y=-9.[/tex]
From the previous statements you can conclude that the graphs have the same shape and the y-intercept of y=|x| is 0, the y-intercept of the second graph is -9.
Answer: correct choice is C.
Unknown digit for 2.84 > 2.4 1 > 2.463
The digit _ that will make 2.4_1 be more than 2.463 must be 7, 8, or 9.
If the first number in your sequence is 2.48 (not 2.84), then the unknown digit must be 7.
2.48 > 2.471 > 2.463
Is 15.5 a irrational or rational number? ANSWER ASAP
Answer: 15.5 is a rational number.
Step-by-step explanation: We are given to check whether the number 15.5 is a rational or irrational.
We know that
a real number is said to be
(i) rational, if the digits after the decimal are either repeating or terminating.
(ii) irrational, if the digits after the decimal are non-repeating and non-repeating.
The given number is 15.5.
Here, the digits after the decimal are terminating.
So, the given number is a rational number.
Thus, 15.5 is a rational number.
the difference between −5y+1 and 3y+2 is equal to −9. find y
Answer:
Step-by-step explanation:
(−5y+1) - (3y+2) = −9
(-5y-3y) + (1-2) = -9
-8y - 1 = -9
-8y = -8
y = 1
the difference between the 2 expressions is
- 5y + 1 - (3y + 2 ) = - 9
- 5y + 1 - 3y - 2 = - 9
- 8y - 1 = - 9 ( add 1 to both sides )
- 8y = - 8 ( divide both sides by - 8 )
y = 1
HURRY PLEASE! Which equation can be used to find the answer? A contractor needs 36 bags of cement to do a job. She already has 17 bags. How many more bags does she need to do the job? A. 2 · b = 36 b = 18 18 bags B. b + 17 = 36 b = 19 19 bags C. b ÷ 2 = 17 b = 34 34 bags D. b – 17 = 36 b = 53 53 bags
the answer is 53 bags
If a circle has radius of 2.5 what would the diameter be
diameter = 5
the diameter is twice the radius
diameter = 2.5 × 2 = 5
Geometry HELP! Please help if your good with geometry. Thanks
Answer:
20a. 143 deg
20b. 37 deg
20c. corresponding angles, congruent
20 d. same-side interior angles, supplementary
Step-by-step explanation:
20a.
m<7 = 34
m<5 + m<7 = 180 (linear pair)
m<5 = 180 - 37 = 143
m<4 = m<5 = 143 (alt int angles)
20b.
m<2 = m<7 = 37 (alt ext angles)
20c. corresponding angles, congruent
20d. same-side interior angles, supplementary
(a)
∠7 = 37° = ∠6 ( vertical angles )
∠4 = 180° - 37° = 143° ( 4 and 6 are supplementary interior angles )
(b)
∠2 = 37° (2 and 4 form a straight angle )
(c)
∠4 and ∠8 are corresponding congruent angles
(d)
∠3 and ∠5 are supplementary interior angles
Two numbers have a sum of 50 If one number is p, express the other number in terms of p.
the other number is 50 - p
Consider a numeric example
2 numbers sum to 5 , one of the numbers is 3 what is the other ?
Obviously 2 , that is 5 - 3 = 2 gives the number
In the same way the number here is p and 50 - p is the other number
A rectangular park has an area of 250 square feet. The length of the park is 7 feet more then twice the width, w of the park. Which equations, in terms of w, model this situation
Area = length * width
width = w
length = 2w+7
A = (2w+7) * w
250 =2w^2+7w
0 = 2w^2 +7w-250
w is the width, hence length is 2w + 7 ( 7 more than twice the width )
area = length × width = w( 2w + 7 ) = 250
2w² + 7w - 250 = 0 ← in standard form
y=x vertical compression compression by a factor of 1/7 please compress the equation of y=x by a vertical compression of 1/7
Answer: y = 1/7(x) or y = x/7
Step-by-step explanation:
Hey there! Thank you for submitting your question to Brainly!
In order to vertically compress the equation y = x by 1/7, we would simply need to multiply x by 1/7. Therefore, this gives us the equation y=1/7(x) or y=x/7.
Hope this helps!! :)
A vertical compression by a factor of 1/7 to the equation y=x results in the new equation y=1/7x where each y-value of the original function is 1/7 of its original height.
Explanation:A vertical compression by a factor of 1/7 to the equation y=x results in the new equation y=1/7x. In vertical compression, each y-value of the original function is multiplied by the factor of compression, in this case, 1/7. Thus y=x becomes y=1/7x. This means for any x value in the original function, the corresponding y value in the new function is 1/7 of its original height. For example, where x was 1, y was also 1 for the original equation. In the new equation, when x is 1, y is now 1/7.
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Christine, Henry, and Manuel have a total of $109 in their wallets. Manuel has 3 times what Christine has. Christine has $9 less than Henry. How much do they have in their wallets?
Christine has $20, Manuel has $60 and Henry has $29
let x be the amount Christine has then
Manuel has 3x and Henry x + 9
summing the amounts gives the equation
x + 3x + x + 9 = 109
5x + 9 = 109 ( subtract 9 from both sides )
5x = 100 ( divide both sides by 5 )
x = 20
thus Christine has $29, Manuel has (3 × 20 ) =$60 and
Henry has 20 + 9 = $29
check : 20 + 60 + 29 = 109
(4x^2-4x-3)+(3x^2-3x-5) then (4x^2-4x-3)-(3x^2-3x-5) show work on both mark brainliest
We have to add the polynomials [tex](4x^2-4x-3)[/tex] and [tex](3x^2-3x-5)[/tex]
To add the polynomials we need to add the like terms, by like terms we understand that the terms with the same exponent of the variables.
So in this case,
[tex](4x^2-4x-3)+(3x^2-3x-5)[/tex]
We will add the coefficients of [tex]x^2, x[/tex], and constants separately, we get:
[tex](4+3)x^2+(-4-3)x+(-3-5)=7x^2+(-7)x+(-8)=7x^2-7x-8[/tex]
Similarly, for the polynomials [tex](4x^2-4x-3)-(3x^2-3x-5)[/tex]
We will subtract the coefficients of like terms, we get:
[tex](4-3)x^2-(4-3)x-(3-5)=x^2-x+2[/tex]
Given the function f(x)=x^2 and k=3, which of the following represents the graph becoming more narrow?
A. f(x)+k
B. kf(x)
C. f(x+k)
D. f(k-x)
B
the spread of the graph of a parabola is determined by the multiplier k
the standard comparison is against k = 1
• If k > 1 then the graph narrows towards the y-axis
• If 0 < k < 1 then graph widens towards the x- axis
An adventure game has a number cube with 12 equal-size faces. Each face is labeled with a number from 1 to 12. What is the probability of rolling a 4 or a multiple of 5? Enter your answer as a fraction, in simplified form, in the box. $\text{Basic}$ $x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$$x\frac{ }{ }$$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
the probability is a ratio of number of relevant outcomes and total number of possible cases.
In this scenario, the relevant outcomes are
4, 5, 10 (and their count is 3)
and the total number of possible outcomes:
12
so the probability is
3/12 = 1/4
the answer is 3/12 cause when you divied 12 by 4 you will get 3 and we know that there is 12 faces on the cube so that gives you the ratio 3/12.
Mr. Tragrr has $500.00 to spend at a bicycle store. All the prices listed down below include tax.
• He buys a new bicycle for $273.98
• He buys 3 new bicycles for $7.23 each and 1 bicycle helmet for $42.36
• He plans to use the remaining money to buy new cycling outyfor $78.12each.
What is the GREATEST number of cycling outfits thatMr. Traeger can buy withthe remaining money?
To answer the question, you need to determine the amount Mr. Traeger has left to spend, then find the maximum number of outfits that will cost less than that remaining amount.
Spent so far:
... 273.98 + 3×7.23 +42.36 = 338.03
Remaining available funds:
... 500.00 -338.03 = 161.97
The cycling outfits are about $80 (slightly less), and this amount is about $160 (slightly more), which is 2 × $80.
Mr. Traeger can buy two (2) cycling outfits with the remaining money.
_____
The remaining money is 161.97/78.12 = 2.0733 times the cost of a cycling outfit. We're sure he has no interest in purchasing a fraction of an outfit, so he can afford to buy 2 outfits.
Sum is 20 quotient is 4
To solve the equation, multiply both sides by 2 and simplify. The value of Qburgers is 5.
Explanation:The question involves solving an equation for the variable Qburgers.
Start by multiplying both sides of the equation by 2 to simplify it.After simplifying, you will be left with 4 times the number of Qburgers and 1 times the number of Qbus tickets equal to 20. Divide both sides of the equation by 4 to isolate and find the value of Qburgers.The value of Qburgers is 5.
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes.
y= 1 3 x− 2 3
You are converting 8 centimeters to meters. How will the number of meters compare to 8? Explain.
Please help I'm timed!
The "meter" is a larger unit than the "centimeter." Every time you need to convert a larger metric unit to a smaller one, you must multiply to find a greater value.
there are 100 cm in a meter so the fraction would be 8/100 or simplified 2/25
Simplify the expression. 12x^-6 y^10 times 3x^7 y
We need to simplify the expression:
[tex]12x^{-6}y^{10} \times (3x^{7}y)[/tex]
Now, we know that we can resolve the exponents of the variables with the like terms only and we can multiply the coefficients independently:
Now,
[tex]12x^{-6}y^{10} \times 3x^{7}y=(12 \times 3)\times (x^{-6}\times x^{7})\times (y^{10}\times y)[/tex]
On simplifying the above expression we get:
[tex]36\times x^{(-6+7)}\times y^{(10+1)}[/tex]
[tex]=36 \times x^{1}\times y^{11}[/tex]
[tex]=36 \times x \times y^{11}[/tex]
[tex]=36xy^{11}[/tex]
So the simplified form of the expression [tex]12x^{-6}y^{10} \times 3x^{7}y=36xy^{11}[/tex].
given that r is the midpoint of qs and that the lenght of qr is 5.7, find the lenght of qs
Answer:
d. 11.4
Step-by-step explanation:
point r is half the line qs. qr is 5.7 so to get the whole line multiply it by two to get 11.4