Answer:
Charlotte's age = 30 years
Olivia's age = 50 years
Step-by-step explanation:
Present ages of Charlotte & Olivia = 6:10.
Then, their present ages are:
Charlotte = 6x
Olivia = 10x
Now, in 10 years, their ratio = 4:6
Then,
Ratio of Charlotte's & Olivia's present age + 10 years each = Ratio of their ages in 10 years
[tex]\frac{6x + 10}{10x + 10} = \frac{4}{6} \\6(6x + 10) = 4 (10x + 10) \: \: \: \: [\mathrm{cross\: multiplication}]\\36x + 60 = 40x + 40\\36x - 40x = 40 - 60\\4x = 20\\\boxed{\bf\:x = 5}[/tex]
So,
Charlotte's present age [tex]= 6x = 6(5) = {\boxed{\bf\:30 \:years}[/tex]
Olivia's present age = [tex]10x = 10(5) = \boxed{\bf\:50 \: years}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Solve using substitution
y= 7x + 6
4x - 3y =16
Answer:
{y,x} = {-8,-2}
Step-by-step explanation:
Hope this helps.
You buy milk at $2.48 per gallon. One portion of oatmeal requires 4 ounces of milk. How much does the milk for one portion cost?
Answer:
$0.01
Step-by-step explanation:
Convert gallons to ounces:
0.03125 Gallons of milk per serving
0.03125/2.48=0.0126008
Simplify:
0.01.
One portion costs 1 cent.
Find the distance between each pair of points.
on graph paper.
K = (-21, -29) and L = (0, 0)
Answer:
~36 units apart
Step-by-step explanation:
(-21 - 0) = -21 (-29 - 0) = -29-21^2 = 441 -29^2 = 841441 + 841 =1282square root of 1282 is 35.8035.80 is ~36~36 units
Helppp I need this asap
Answer:
[tex]x = 35[/tex]
Step-by-step explanation:
We can use Similar Triangles Ratios to solve for the missing side length. First setup your ratios:
[tex]\frac{42}{6} = \frac{x}{5}\\x = \frac{42}{6} \times 5\\x = 35[/tex]
Answer:
35
Step-by-step explanation:
The sides are in proportion.
[tex]\frac{AB}{PQ} =\frac{AC}{PR}[/tex]? / 5 = 42 / 6? = 5 × 7? = 35A camera has a listed price of $615.99 before tax. If the sales tax rate is 9.25%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
559.01 i think that is rounded correctly
Step-by-step explanation:
so it did $615.99 - 9.25% = 559.010925
Hope This Is Good And Helped Sorry If i Did It Worng
a) How many 2-digit numbers have the digit 7 exactly once?
Answer:
17, 27, 37, 47, 57, 67, 87, 97.
8
Step-by-step explanation:
all are 2 digit numbers with exactly one 7 in each.
Answer:
8
Step-by-step explanation:
the two digit numbers that has 7 exactly once are 17, 27, 37, 47, 57, 67, , 87, 97from above, there are 8 two digitsPlease help, image below. Thank you!
Answer:
10 Inches
Hope it helps, have a fantastic day.
Step-by-step explanation:
The Circumference of a circle can be displayed by this formula:
[tex]C = 2\pi r[/tex]
[tex]C[/tex] is the circumference, and [tex]r[/tex] is the radius.
So just plug in 31 for [tex]C[/tex], and simplify:
[tex]31 = 2\pi r[/tex]
Because the question is asking for the diameter, we only need to divide both sides by pi, as [tex]2r[/tex] is the same thing as diameter.
[tex]9.87 = 2r[/tex] (rounded to the nearest hundredth)
We can even rewrite [tex]2r[/tex] as [tex]d[/tex], which stands for diameter, to make things a little simpler.
[tex]9.87 = d[/tex]
Now we just take 9.87, and round it to the nearest whole number, and we get 10. So your answer is 10 Inches.
Hope it helps, have a fantastic day.
How many pounds of walnuts that cost $0.80 per pound must be mixed
with 8 pounds of cashews that costs $1.25 per pound to make a mixture of
nuts that costs $1.00 per pound?
Answer:
The number of walnut pounds we need to add is 10
Step-by-step explanation:
We need to make a mixture that costs $1 per pound.
That means that the total cost of our mixture, divided by the number of pounds must be equal to 1.
[tex]\frac{MixtureCost}{NumberOfPounds} = 1[/tex]
Well, we know that the total cost of our mixture is equal to the cost of the cashews + cost of walnuts.
[tex]MixtureCost = CashewsCost + WalnutsCost[/tex]
We also know that we'll buy 8 pounds of cashews that cost $1.25 each and some amount of pounds (which we'll call x) of walnuts that cost $0.80.
Knowing all of that, we can write this:
[tex]MixtureCost=8*1.25 + x*0.8[/tex]
If we make that multiplication, we have that
[tex]MixtureCost=10+x*0.8[/tex]
Now that we know the cost of our mixture, we just need to know the total number of pounds... But we already know that, don't we?
We know that there are 8 pounds of cashews and x pounds of walnuts, so here's what we can write:
[tex]NumberOfPounds=8+x[/tex]
Now, if we plug in the values we found in the first equation, here's what we have:
[tex]\frac{10+x*0.8}{8+x}=1[/tex]
The 8+x is dividing, so i'll pass it to the other side multiplying:
[tex]10+0.8*x=x+8[/tex]
The 10 in the left side will go to the right side with a negative sign:
[tex]0.8x=x-2[/tex]
Now, if I pass the x from the right side to the left one changing signs:
[tex]0.8x-x=-2\\\\-0.2x=-2[/tex]
By changing signs from both sides, we have that:
[tex]0.2x = 2\\\\x = 10[/tex]
Therefore, the number of walnut pounds we need to add is 10
what equation represents the graph
Answer:
y = (x + 1)(x - 2)(x -3)
Step-by-step explanation:
Looking at the graph we see our zeros which is on the x-axis is -1 , 2, 3.
Thus create an equation.
y = (x + 1)(x - 2)(x -3)
Which of the following is not a real number?
A. √2
B. -2
C. √₁,
D. 0
what percent of 7 is 3.5
Answer:
50%Step-by-step explanation:
what percent of 7 is 3.5
3.5 is half of 7, so 100%: 2 = 50%
Answer: 50%
I have shown two methods, both work well and can be used to solve other scenarios as well.
[Method One]
We will set up a proportion and solve.
-> A percent divided by 100 is a decimal. This means 100% = 1 in our proportion
[tex]\frac{1}{7} =\frac{x}{3.5}[/tex]
7x = 3.5
x = 0.5
0.5 * 100 = 50%
[Method Two]
We will put the whole value in the denominator, and the "what percent of" value is the numerator.
[tex]\displaystyle \frac{3.5}{7}[/tex]
0.5
0.5 * 100 = 50%
Check the picture of the necessary information
suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 4 inches. The heights of 10 randomly selected students are 66, 61, 67, 61, 75, 71, 70, 61, 61, and 74
A mean is an arithmetic average of a set of observations. The height of the 9th-grade students will be 66.7±4 inches.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
Given the height of the 10 selected students is {66, 61, 67, 61, 75, 71, 70, 61, 61, and 74}, also, the standard deviation of the 9th-grade students is 4 inches. Therefore, The mean height in inches of the selected students is,
Mean = (66+61+67+61+75+71+70+61+64)/10 = 66.7inches
Therefore, the height of the 9th-grade students will be 66.7±4 inches.
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Write the equation of the circle graphed below
Answer:
were is the circle to be to be equated
help will mark Brainliest
Answer:
C. is the correct answer
Step-by-step explanation:
A. is incorrect because the sequence does not start with 15
B. is incorrect because the pattern increases by 5, not multiplied by 5
C. is correct because all of the even numbers in the pattern do end in 0
D. is incorrect because even numbers don't end in 5's
Hope this helps!
Answer: "Every even-numbered term in the pattern has a 0 in the evens place"
Step-by-step explanation:
We can compare each statement to the pattern and see which ones don't apply.
The first one is not true. We are adding 5, not having a sum of previous numbers.
The second one is not true, it is adding 5. Not 5 times greater.
An even number is a number ending in 0, 2, 4, 6, or 8. This means
that the third option is correct, giving us our answer.
16. Farhan bought a bag and a wallet at a discount from a store. He was
given a discount of 30% for the bag. For the wallet, a discount was also
given. He saved a total of $66.60.
He paid a total of $121.40 for the 2 items and paid $46.60 more for the
bag than the wallet.
a) What was the price of the bag without discount?
b) What was the percentage discount given for the wallet?
A) the price of the bag without discount was $120, and B) the discount on the wallet was 45%.
PercentagesGiven that Farhan bought a bag and a wallet at a discount from a store, and he was given a discount of 30% for the bag, and for the wallet, a discount was also given, and he saved a total of $66.60, and he paid a total of $121.40 for the 2 items and paid $46.60 more for the bag than the wallet, to determine A) what was the price of the bag without discount, and B) what was the percentage discount given for the wallet, the following calculations must be performed:
(121.4 - 46.6) / 2 = Wallet37.4 = Wallet1-0.3 = 0.70.7 = 841 = X84 / 0.7 = X120 = X66.6 - (120 - 84) = X66.6 - 36 = X30.6 = X68 = 10037.4 = X37.4 x 100 / 68 = X55 = XTherefore, A) the price of the bag without discount was $120, and B) the discount on the wallet was 45%.
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Answer:A) the price of the bag without discount was $120, and B) the discount on the wallet was 45%.
Step-by-step explanation:
Five workers together can build a road in 20 days. Suppose every worker works at the same rate. Three workers work on the road for 10 days before eleven more workers join them. How much longer will it take the fourteen workers to finish the road?
Answer:
5 days
Step-by-step explanation:
This problem is an inverse proportion case. Having two variables: number of workers and time (in days); when we increase the number of workers, the time needed decreases; vice versa. Therefore, we can use the multiplication method: (workers * time) will always stay constant.
Let's say the time (in days) needed by the eleven workers is t,
5*20 = (3*10) + (14*t)
100 = 30+14t
70 = 14t
5 = t
It will take the eleven-workers 5 more days to finish the road.
Determine the equation of the line that has an x-intercept of 6 and passes through the point (6,4)
Pls help urgent i will marke the brainlist
Answer:
Yes, because 8n + 4 = 4(2n + 1) because of the distributive property. And about the 4 = 52 - 8n, that is also equivalent to the rest of them because of the associative property.
OR
You could just solve the math and show that they are equivalent.
Calculus, factor the given polynomial.
Answer:
x² + 10x + 21 = (x + 3)(x + 7)Step-by-step explanation:
x² + 10x + 21 = x² + (3x + 7x) + 21
= (x² + 3x) + (7x + 21)
= x(x + 3) + 7(x + 3)
= (x + 3)(x + 7)
Determine the equation of the circle graphed below.
10
8
6
4
2
-10 -B -6
8
-4
-2
-2
4
-6
-8
-10
2
4
10
Answer: (x +7)^2 +(y +6)^2 = 9
Step-by-step explanation:
The given circle appears to be centered at (-7, -6) and have a radius of 3. The standard form equation of a circle is ...
(x -h)^2 +(y -k)^2 = r^2 . . . . . . circle of radius r centered at (h, k)
For (h, k) = (-7, -6) and r=3, your circle is ...
(x -(-7))^2 +(y -(-6))^3 = 3^2
(x +7)^2 +(y +6)^2 = 9
i hope this helps btw i did not copy n paste l got 100% on this
Write the symbolic expression for each of the following descriptions, then get rid of the radical and make them exponential expressions in fractional form.
11. The eighth root of fifty-seven to the sixth degree
12. The square root of Y to the fourteenth degree
13. The nth root of m to the o plus p degree.
14. The fifth root plus x of eighty-one to the third power.
15. The cube root of five squared.
Answer:
11. [tex]57^{6/8}[/tex]
12. [tex]Y^{14/2}[/tex]
13. [tex]m^{\frac{o+p}{n}}[/tex]
14. [tex]81^{\frac{3}{50+x}}[/tex]
15. [tex]5^{2/3}[/tex]
Step-by-step explanation:
When converting from radicals to rational exponents, there's a quick, easy rule to remember:
[tex]\sqrt[n]{x} =\sqrt[\text{index}]{\text{radicand}}[/tex] the exponent is [tex]\frac{\text{power}}{\text{root}}[/tex][tex]\sqrt[n]{x} = x^{1/n}[/tex]The "power" represents the exponent of the radical/radicand, while the "root" represents the index.
11. the eight root of fifty-seven to the sixth degree.
Write the expression in radical form: [tex]\sqrt[8]{57^6}[/tex]Rewrite using the exponent rule (power over root): [tex]57^{6/8}[/tex]12. the square root of Y to the fourteenth power.
Write the expression in radical form: [tex]\sqrt[2]{Y^{14}}[/tex]Rewrite using the exponent rule (power over root): [tex]Y^{14/2}[/tex]13. the nth root of m to the o plus p degree.
Write the expression in radical form: [tex]\sqrt[n]{m^{o+p}}[/tex]Rewrite using the exponent rule (power over root): [tex]m^{\frac{o+p}{n}}[/tex]14. The fifth root plus x of eighty-one to the third power.
Write the expression in radical form: [tex]\sqrt[5+x]{81^{3}}[/tex]Rewrite using the exponent rule (power over root): [tex]81^{\frac{3}{50+x}}[/tex]15. The cube root of five squared.
Write the expression in radical form: [tex]\sqrt[3]{5^{2}}[/tex]Rewrite using the exponent rule (power over root): [tex]5^{2/3}[/tex]if (2x+5,7)=(7,y), find the value of x and y
[tex]\text{Given that,}~ (2x+5, 7)=(7,y)\\\\\text{So,}~ y = 7 ~ \text{and}~2x +5 = 7\\\\~~~~~~~~2x+ 5=7 \\\\\implies 2x = 7- 5 \\\\\implies 2x = 2\\\\\implies x = \dfrac 22 \\\\\implies x = 1\\\\\text{Hence,}~~ x = 1 ~ \text{and}~ y = 7[/tex]
please solve the problem
I want whole process
Answer:
1
Step-by-step explanation:
⠀
⠀
⠀⠀⠀⠀□ Question[tex] \Large \frac{ {x}^{p(q - r)} }{ {x}^{q(p - r)} } \div {( \frac{ {x}^{q} }{{x}^{p} } })^{r} [/tex]
⠀
⠀
⠀⠀⠀⠀■ Solution⠀
Multiplying the power⠀
[tex] \sf \Large{ \frac{ {x}^{pq - pr} }{ {x}^{pq - qr} } } \div \frac{ {x}^{qr} }{ {x}^{pr} } [/tex]
⠀
⠀
Changing ÷ sign into × by doing reciprocal⠀
[tex] \sf\Large{ \frac{ {x}^{pq - pr} }{ {x}^{pq - qr} } } \times \frac{ {x}^{pr} }{ {x}^{qr} } [/tex]
⠀
⠀
As the base(x) is same, if the value is multipying so the power will add, if the value is dividing so the power will subtract.⠀
[tex] \sf {x}^{pq - pr - pq + qr} \times {x}^{pr - qr} \\ \\ \sf {x}^{qr - pr} \times {x}^{pr - qr} \\ \\ \sf {x}^{qr - qr + pr - pr} [/tex]
⠀
⠀
If the power of any value become 0,so it's value is always equal to 1⠀
[tex] \sf \Large{ {x}^{0} } \\ \\ \boxed {\large {\rightarrow1 }}[/tex]
Answer:
1
Step-by-step explanation:
Solving :
⇒ [tex]\frac{x^{p(q-r)} }{x^{q(p-r)} }[/tex] ÷ [tex](\frac{x^{q} }{x^{p} })^{r}[/tex]
⇒ [tex]\frac{x^{p(q-r)} }{x^{q(p-r)} }[/tex] ÷ [tex][ ({x^{q-p} })^{r}| or| x^{r(q-p)} ][/tex]
⇒ [tex]{x}^{pq-pr-qp+qr}[/tex] ÷ [tex]x^{rq-rp}[/tex]
⇒ [tex]x^{pq-pq+qr-qr+pr-pr}[/tex]
⇒ x⁰
⇒ 1
really need help with my aleks
Answer:
(4x -4)° +x° +(6x-3)° = 180°J = 99°K = 64°L = 17°Step-by-step explanation:
The relation that helps you write an equation for x is, "the sum of angles in a triangle is 180°."
__
equation(4x -4)° +x° +(6x -3)° = 180° . . . . . sum of angles in this triangle
solution for x11x -7 = 180 . . . . . . . divide by °, collect terms
11x = 187 . . . . . . . . add 7
x = 17 . . . . . . . . . divide by 11
angle valuesm∠J = (6x -3)° = (6(17) -3)° = 99°
m∠K = (4x -4)° = (4(17) -4)° = 64°
m∠L = x° = 17°
solve by completing the square
Step-by-step explanation:
[tex] {x}^{2} + 2x - 2 = 0[/tex]
Now Adding three on both sides we get
[tex]{x}^{2} + 2x - 2 + 3 = 0 + 3[/tex]
[tex] {x}^{2} + 2x + 1 = 3[/tex]
[tex] {(x + 1)}^{2} = 3[/tex]
Find P(Not a 3).
A. 0.30
B. 0.15
c. 0.85
D. 0.70
Answer:
P(Not a 3)=0.85. This is option C.
Step-by-step explanation:
P(Not a 3) would include values 1,2 and 4.
Therefore, P(Not a 3) would be the combined totals of the probabilities of P(1), P(2) and P(4).
P(Not a 3)= P(1)+P(2)+P(4)
P(Not a 3)= 0.30+0.40+0.15
P(Not a 3)=0.85
Alternate method
P(Not a 3) is the same as 1-P(3)
P(Not a 3)=1-P(3)
P(Not a 3)= 1-0.15
P(Not a 3)=0.85
N
The accurate scale drawing shows
the positions of port P and a lighthouse L.
►
c)
N
Lindsey sails her boat from port P
on a bearing of 050°
She sails for 12 hours at an average
speed of 5 km/h to a port Q.
Ito-
L
p*
Scale: 1 cm represents 3 km.
a) Indicate the position of port Q on the drawing (use the x tool).
(2)
b) Find the distance, in km, of port Q from lighthouse L.
(1)
c) Find the bearing of port Q from lighthouse L.
)
(2)
Total marks: 5
Feedback
The Indication of the position of port Q on the drawing is shown by using the example of the image attached.
What is the distance about?To Indicate the position of port Q on the drawing (use the x tool).
12 * 5 = 60km
Note that S= VT
Because 1cm represent 3km
1/3 =x/60
3x = 60
x= 60/3
x= 20
So therefore, 60km needs 20cm.
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Suppose your friend's parents invest $ 10,000 in an account paying 5% compounded annually. What will the balance be after 8 years?
Answer:
A = $14,745.544
Step-by-step explanation:
The equation for compound interest is
A = P (1+i)t
A = final value
P = amount invested (principal) (10000)
i = interest rate, expressed as a decimal (.05)
t = number of years invested (8)
This formula assumes annual compounding.
Plugging in what we know.
A = 10000(1.05)^8
A = 10000 (1.47745544)
A = $14,745.544
how many numbers between 75 and 500 are divisible by 7?
