If the product of two positive integers is 180 and the larger number is 5 times the smaller number, what are the numbers

Answers

Answer 1

Let the smaller number be x
The bigger number is 5x

5x(x) = 180
5x² = 180
x² = 180÷5
x²=36
x=√36
x = 6

x=6
5x = 6 x 5
5x = 30

So the two numbers are 6 and 30

Related Questions

Dione has 3 rolls of pennies containing 50 coins each, 4 rolls of nickels containing 40 coins each, 5 rolls of dimes containing 50 coins each, and 6 rolls of quarters containing 40 coins each. How much money does she have?

A. $106.20
B. $17.50
C. $8.00
D. $94.50

Answers

the total number of pennies she has - 3 x 50 = 150
value of penny - $ 0.01
value she has from pennies - $0.01 x 150 = $1.50

total number of nickels she has - 4 x40 = 160
value of nickel - $ 0.05
value she has from nickels - $0.05 x 160 = $8

total number of dimes she has - 5 x 50 = 250
value of dime - $ 0.10
value she has from dimes - $0.10 x 250 = $25

total number of quarters she has - 6 x 40 = 240
value of quarter - $ 0.25
value she has - $ 0.25 x 240 = $ 60

total amount of money she has = 1.50 + 8 + 25 + 60
money she has = $ 94.50
correct answer is D

Please help, I’m kinda confused

Answers

I'm not sure, but I think is 15 :/ Hope it helped

What is the value of the missing number in the sequence below? 4, 12, 36,___, 324, 972, 2916

Answers

The sequence increases by multiplying the previous number by 3. 4*3=12 12*3=36 36*3=108 and so on. The missing number is 108

The missing number will be 108. The sequence is; 4, 12, 36,108, 324, 972, 2916.

What is a sequence?

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The given sequence is;

4, 12, 36,108, 324, 972, 2916

It is observed from the sequence that the following sequence follow a specific rule in which the progressive term is multiplied by a factor of 3.

[tex]\rm 4 \times 3 = 12 \\\\ 12 \times 3 = 36 \\\\ 36 \times 3 =108[/tex]

Hence, the missing number will be 108.

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ2

angle measure represented by 4.5 rotations counterclockwise

Answers

keeping in mind that, angles are measured counter-clockwise, namely in the opposite direction of a clock, if you have a clock, notice the seconds hand how it moves, well, counter to that is going backwards, but that's how angles are regularly measured.

now, a full rotation, namely a "revolution", is a full go-around the circle, that'd be 360°, now if you 4 times around, that be 4*360 or 1440°, and if you go an extra 0.5 or half a circle, that'd be 180°, that will land us on 1440° + 180°.

Hey can somebody help me? I know it seems easy but I forgot the process on how to do this. Thanks in advance!
---------------------------------
1 1/2 - 1/2 = ???

Show your work please so I understand

Answers

Since we can break down 1 1/2 into 1 + 1/2, and we know that 1/2 - 1/2 = 0, we can just add one. So, the answer is 1.

Sorry if this was a bit unclear, I did my best to explain ;)

Hope this helps!

Easy Algebra 2 Rational Expressions question

Answers

IF it is nonpermissible then we are checking the denominator to see where it equals 0 at

y - 3 = 0
y = 3 - this is where the fraction is undefined (or nonpermissible)

Russ is constructing the inscribed circle for △ABC . He has already used his compass and straightedge to complete the part of the construction shown in the figure.
What could be his next step?

A)Use the straightedge to draw a line through point N that intersects BC¯¯¯¯¯ .
B) Use the straightedge to draw the line through points M and P.
C) Place the point of the compass on point C and draw an arc that intersects AC¯¯¯¯¯ and BC¯¯¯¯¯ .
D)Place the point of the compass on point N and draw an arc that intersects AB¯¯¯¯¯ and BC¯¯¯¯¯ .

Answers

The answer is C.

Place the point of the compass on point C and draw an arc that intersects AC¯¯¯¯¯ and BC¯¯¯¯¯ .

Answer: The answer is (C) Place the point of the compass on point C and draw an arc that intersects AC and BC.

Step-by-step explanation: Given that Russ is constructing the inscribed circle for △ABC and he has already used his compass and straightedge to complete the part of the construction shown in the given figure. We are to find his next step.

Since Russ has already constructed the angle bisector of ∠B, so next he shoul construct the angle bisector of either ∠A or ∠C. Since the steps for constructing angle bisector of ∠A are not in the options, so he should go with ∠C. For that, he must place the point of the compass on the point C and draw an arc that intersects AC and BC.

Thus, (C) is the correct option.

how is jimthompson so smart?

Also can you please help me with that question.
I got everything except for the Euler Diagram.

Answers

The statement is valid. To set up a Euler diagram, follow these steps

Step 1) Draw a large circle and label it circle A

Step 2) Inside this large circle, draw a smaller circle and label it circle B

Circle A will represent the set of all obtuse angles (any angles that are between 90 and 180 degrees). Circle B represents only one item: the angle value of 150 degrees. All of circle B is inside circle A because 150 degrees is between 90 and 180; therefore, 150 is obtuse. This is simply the definition of what "obtuse" means.

So if you threw a dart and it landed in circle B, then you know for sure it landed in circle A as well. This is effectively saying "if you get a 150 degree angle, then you know its obtuse"

This is a visual way to back up the conditional statements you used earlier and help add more evidence that the statement "A 150 degree angle is an obtuse angle" is a valid statement.

Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X?

Answers

supplementary angles sum = 180
lets x = measure of angle Y

x + 3x = 180
4x = 180
x = 45

angle Y = 45
angle X = 3 x 45 = 135

answer
Angle X = 135

Answer:

The measure of ∠X is 135°

Step-by-step explanation:

Given that angles X and Y are supplementary and also angle X is 3 times the measure of angle Y.

we have to find the measure of angle X.

Since X and Y are the supplementary therefore these add up to 180° i.e

[tex]\angle X+\angle Y=180\°......(1)[/tex]

Also angle X is 3 times the measure of angle Y i.e

[tex]\angle X=3\angle Y[/tex]

Substitute this value in equation (1), we get

[tex]3\angle Y+\angle Y=180\°......(1)[/tex]

[tex]4\angle Y= 180\°[/tex]

[tex]\angle Y=\frac{180\°}{4}=45\°[/tex]

[tex]\angle X=3\times 45\°=135\° [/tex]

Hence, the measure of ∠X is 135°

A $6,300.00 principal earns 6% interest, compounded annually. After 3 years, what is the balance in the account?

Answers

7,503

Hope this helped!

Hello,

To find this answer, you have to start with 6,300 and multiply it by 1.06 three times. We are using 1.06 because we are adding 6% (0.06) onto the total 3 times.

6300 x 1.06 x 1.06 x 1.06 = $7,503.40
OR
6300(1.06)^3 = $7,503.40

The second equation is written as a compound interest equation. You just need to switch the 3 if you want to find the total for a different amount of years.

I hope this helps, Good luck!

In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 7 in?
Enter your answer in the box.

Answers

14 inches. A 30-60-90 triangle has a set ratio for the sides which is x:x√3:2x for the sides opposite the corresponding angle. (30 = x, 60 = x√3, 90 =2x) the shortest side is the side opposite the 30-degree angle so x=7. The hypotenuse is the side opposite the 90-degree angle. they hypotenuse = 2x. Substitute x. 2(7)=14

The length of the hypotenuse is 14in

SOH CAH TOA identity

Given a 30-60-90 triangle where:

Length of the shorter leg = 5cm (adjacent)

The hypotenuse is what we need..

[tex]cos \theta = \frac{adj}{hyp} \\ [/tex]

Substitute the given parameters

[tex]cos 60 = \frac{7}{h}\\ h =\frac{7}{cos 60}\\ h = \frac{7}{0.5}\\ h = 14in\\ [/tex]

Hence the length of the hypotenuse is 14in

Learn more on SOH CAH TOA here: https://brainly.com/question/20734777

At the beginning of an experiment, there are 600 grams of contaminants. Each hour, half of the contaminants are filtered out. How many grams of contaminants remain after 4 hours?

Answers

37.5 grams of contaminants will remain after 4 hours.

First hour - 300
Second hour - 150
Third hour - 75
Fourth hour - 37.5

I need help with this as well

Answers

n 19 -----------> AB/AC=(4/6)=2/3

n 20 ------------> BC/CD=[AC-AB]/[AD-AC]=(6-4)/(9-6)=2/3

n 21-------------> BD/AE=[AD-AB]/[AE]=(9-4)/(12)=5/12

n 22 7 and 28 find the geometric mean of the two number
step 1
Multiply the two numbers together:
28*7=196
step 2
take the square root:
sqrt(196)=14
the answer is 14

n 23 Simplify the ratio 10 ft/30 in---> divided between 2 both members
5 ft/15 in-----> divided between 5 both members ---> 1 ft/3 in

n 24
if AB=4 -------> AB~FG
FG=8
then
AB*factor=FG-------- > 4*factor=8-- > factor=8/4=2
the figure ABCDE is half of the figure FGHJK
then
BC=4
AE=CD=5
and
ED=6
therefore
the perimeter=[4+4+5+5+6]=24 units

Please help me, i don't understand how to do this.
Solve V = 1 3 πr2h for h.
A) 3V πr2
B) V 3πr2
C) r sqrt 3V π
D) V - 1/3 πr2

Answers

1/3 *(πr2h) = v πr2h/3 = 3

so h = 3v/πr2

Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up. What are the coordinates of B' after the translation?
a.(1, 6)
b.(–3, 6)
c.(0, 0)
d.(3, 1)

Answers

the coordinates are -3 , 6

Answer:

b. [tex](-3,6)[/tex]

Step-by-step explanation:

We have been given that triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up.

To find the coordinates of B', we will shift x-coordinate of point B to left by 3 units and y-coordinate of point B to 1 unit up.

After the given transformation the coordinates of point B' would be:

[tex]B(0,5)\rightarrow B'((0-3),(5+1))\rightarrow (-3,6)[/tex]

Therefore, the coordinates of point B' are [tex](-3,6)[/tex] and option 'b' is the correct choice.

What is the image of the point (4,-2) after a rotation 270 degree clockwise about the origin?

Answers

The equivalent 90° CCW rotation maps (x, y) to (-y, x).
(4, -2) becomes (2, 4) after rotation.

Answer:

The image of the point (4, -2) is (2, 4).

Step-by-step explanation:

Since, the rule of rotation 270 degree clockwise about the origin is,

[tex](x,y)\rightarrow (-y,x)[/tex]

Where, (-y,x) is the image of the point (x,y),

Thus, by the above rule,

[tex](4,-2)\rightarrow (-(-2), 4)[/tex]

Hence, the image of the point (4, -2) is (2, 4).

An artist drew a rectangle. the artist then modified the rectangle so thatthe length ofthe rectawngle increased by 30 percent and the width of the rectangle decreased by 40 percent. after the modification, what was the percent decrease in the area of the rectangle?

Answers

the dimensions of the original rectangle
length - L
width - W
area = L*W = LW
after the modification, new dimensions are
length increased by 30 %
Length = L * 1.3 = 1.3L
Width = W * 0.6 = 0.6W
new area = 1.3L * 0.6W
= 0.78LW
the percent decrease in area
decrease % = (difference in area)/original area * 100
= (LW - 0.78LW)/LW * 100
= 0.22LW/LW * 100
= 22%
percent decrease is 22%

A child walks due east on the deck of a ship at 4 miles per hour.
The ship is moving north at a speed of 12 miles per hour.

Find the speed and direction of the child relative to the surface of the water.

Speed = mph

The angle of the direction from the north = (radians)
i have the speed i couldn't find the direction !,

Answers

If you drew the two vectors for the velocity you find a triangle rectangle since the two directions East and North form an angle of 90°. I drew first the vector towards East and second the vector towards North.

Therefore, to get the speed relative to the surface you have to sum the two vectors, which means you can apply the Pythagorean theorem to find the hypotenuse, having the two legs.

h = √(4² + 12²) = √160 = 4√10 = 12.65mph

In order to find the direction, you need to use trigonometry:
- the sine of an angle is given by the ratio between the opposite side divided the hypotenuse;
- the cosine of an angle is given by the ratio between the adjacent side divided by the hypotenuse.

You can use either one, I will show you both:
sinα = O / H
inverting the formula: α = arcsin (O / H) = sin⁻¹ (O / H)
these two forms are equivalent.

Similarly:
cosβ = A / H
β = arccos (A / H) = cos⁻¹ (A / H).

Substituting your numbers:
α = sin⁻¹ (12 / 12.65) = sin⁻¹ (0.9486) = 1.25rad
β = cos⁻¹ (4 / 12.65) = cos⁻¹ (0.3162) = 1.25rad

As you can see, α = β so you can use either formula.

Your answer will then be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 1.25rad from East towards North.

ATTENTION!
If you drew first the vector towards North and then the one towards East, you get an equivalent triangle, which is rotated by 180° respect to the previous one. This way, what you earlier called Opposite is now Adjacent and vice-versa, but the formulas are still valid.
You will get:
α = sin⁻¹ (4 / 12.65) = sin⁻¹ (0.3162) = 0.32rad
β = cos⁻¹ (12 / 12.65) = cos⁻¹ (0.9486) = 0.32rad
And your answer will be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 0.32rad from North towards East.

is -3 larger than -2?
only answer if you know and not for the points

Answers

Hey there!

Your answer is no.
-3 is not larger than -2. This is because the larger the number is with a negative sign, the smaller the number is!

Hope this helps you.
Have a great day!

Hello there!

No.

-3 is not greater than -2.

When we are speaking about negative numbers, the "lower" the number is, the greater. -2 is greater than -3 because it is closer to the positive side than negative side. -3 is farther away from 0. But as for -2, is alot closer to 0 than -3.

Your answer, No.

I hope this helps you!

The function below can be used to calculate the cost of making a long distance call, f(m), which is based on a $2.50 initial charge and a fee of $.12 per minute, m, that the call lasts. If Natalie paid $6.82 for one call, how many minutes long was it?

Answers

f(m) = 2.5 + 0.12m

if Natalie paid $6.82

6.82 = 2.5 + 0.12m
0.12m = 6.82 - 2.5
0.12m = 4.32
m = 4.32 ÷ 0.12
m = 36

The call was 36 minutes long.

Gina pumps 40 cubic inches of air per second into a balloon. The function below shows the total amount of air f(t) inside the balloon after t seconds. f(w) = 40t + 5 Which statement best describes the y-intercept of the graph of the function?

Answers

The y-intercept of the graph of the function is the initial amount of air inside the balloon (5 cubic inches)

For this case, the first thing you should know is that the intersection with the y-axis occurs when the time equals zero.
Mathematically we have:
For t = 0:
f (0) = 40 (0) + 5
f (0) = 0 + 5
f (0) = 5
Answer:
The intersection with the y-axis represents the total amount of initial air before starting to pump air.
The initial air quantity is:
5 in ^ 3

A set of 5 numbers has a mode of 12 a median of 11 a mean of 10 what could the numbers be?

Answers

The median is 11, so 11 is part of the data set. We have an odd number of values (5) which is why the median is part of the data set.

The mode is 12. The value 12 shows up the most times. Let's say it shows up twice. So far the data set is {11, 12, 12}

Let's introduce two more numbers x and y
The new data set is {x, y, 11, 12, 12}

Add up the five values and then divide by 5. We want this result to be equal to 10
(x+y+11+12+12)/5 = 10
(x+y+35)/5 = 10
x+y+35 = 10*5
x+y+35 = 50
x+y = 50-35
x+y = 15

So we don't know what x or y is, but we know that they must add to 15. So all you have to do is list two numbers that add to 15. One such pair is x = 6 and y = 9. Another pair is x = 7 and y = 8. There are infinitely many possibilities if you can use any real number.

So one possible set is {6, 9, 11, 12, 12}
Another possible set is {7, 8, 11, 12, 12}

A possible answer is 6, 9, 11, 12, and 12. Hope I helped (:

Which of the following decimal numbers equals 4 thousand, 9 hundreds, 2 tens, and 6 ones?

Answers

we have
decimal numbers equals
4 thousand---------> 4000
9 hundreds--------> 900
2 tens-----------> 20
6 ones-------> 6
so
[4000+900+20+6]=4926

the answer is 4926

Out of 1100 discs tested 13 are defective. Estimate the number of defective discs in a batch of 41000

Answers

I’d say 485 discs are defective out of 41000

Where is the vertex of the parabola?

y = x2 + 6x + 7

above the x-axis

on the x-axis

on the y-axis

below the x-axis

Answers

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ \begin{array}{llcccl} y = & 1x^2& +6x& +7\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array} \qquad \left(-\cfrac{ b}{2 a}\quad ,\quad c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{6}{2(1)}~~,~~7-\cfrac{6^2}{4(1)} \right)\implies (-3~~,~~7-9)\implies (-3~~,~~-2)[/tex]

Answer:

below the x axis

Step-by-step explanation:

i took the test

A wood frame costs $1.50. Use a property to write an equivalent expression for the cost of a wood frame.

Answers

Let the width of the frame = x
Let the cost of a linear foot of the frame = y
Let the inside dimension of the length of the frame = a
Let the inside dimension of the width of the frame = b.

The total length of the frame = 2*a + 4x
The total width of the frame = 2b

The total amount of the frame in feet is (2a + 4x + 2b)*y = Cost
If this is incorrect please leave a message on my home page.

Can anyone help me I don’t know how to do this

Answers

Start with the vertex form of the equation of a quadratic. Fill in the numbers you know and solve for the one you don't know.
y = a(x -h)² +k . . . . . . . . for some stretch factor "a" and vertex (h, k)

1. Vertex = (h, k) = (0, 0). Stretch factor can be found from the given point (x, y).
8 = a(-2 -0)² +0
8 = 4a . . . . . . . . simplify
2 = a . . . . . . . . . divide by the coefficient of "a"
Your equation is y = 2x².

Note the above method for solving these problems. It repeats.

2. As above, substitute what's given and solve for what's not.
3 = a(1 -2)² +0
3 = a
Your equation is y = 3(x -2)²

3. Repeat
-4 = a(-5 +3)² +0
-4 = 4a
-1 = a
Your equation is y = -(x +3)²

4. Are you seeing the pattern yet?
0 = a(-1 -0)² +1
0 = a +1
-1 = a
Your equation is y = -x² +1

5 & 6. You know that if you want a zero (x-intercept) to be located at x=a, then a factor of the quadratic will be (x -a). Multiply the factors together to get your quadratic function.

5. y = (x -0)*(x -2) = x² -2x

6. y = (x +5)*(x -5) = x² -25 . . . . . . . . . . you should recognize this "special form", the factoring of the difference of squares

A hair salon charges a fixed rate of $25.00 for a haircut and an additional $15 for any other services. Write a function to model the cost of services at the salon and then evaluate the function to determine the cost for a haircut, shampoo, highlight, and blow dry.

Answers

25+15•3= 70 dollars she spent on the hair salon..... dang lotsa money

Answer:

Function : Cost =25 + 15x

Cost for a haircut, shampoo, highlight, and blow dry = $70

Step-by-step explanation:

Hi, to answer this we have to write an equation:

The cost of the services will be equal to the fixed cost for the haircut (25.00) plus the product of the number of additional services (x) and the price of each additional service (15).

Mathematically speaking:

Cost =25 + 15x

To determine the cost for a haircut, shampoo, highlight, and blow dry, we have to substitute x = 3 (because shampoo, highlight, and blow dry are additional services ) in the equation and solve.

Cost = 25+ 15 (3)

Cost = 25+45

Cost = $70

How do I solve for h

Answers

All the triangles are similar, so the ratio of (long leg)/(short leg) is the same. The long leg of ΔADB is
.. AD = AC -DC = 20 -4
.. AD = 16

Then
.. (long leg)/(short leg) = AD/DB = BD/DC
.. 16/h = h/4
.. h^2 = 64
.. h = 8

Selection D is appropriate.

_____
You may see this again. The altitude (h) from the right angle in a right triangle is the geometric mean of segments AD and DC. That is,
.. h = √((AD)*(DC))

Jana finished 1/4 of her homework at school and 2/3 of it before dinner. How much of her homework has she finished so far?

Answers

1/4+2/3
1/4×3/3+2/3×4/4
3/12+8/12
11/12

Final answer:

Jana has completed 11/12 or 11 out of 12 of her homework so far.

Explanation:

To find out how much of her homework Jana has finished so far, we need to add together the fractions of her homework completed at school and before dinner.

Jana finished 1/4 of her homework at school and 2/3 of it before dinner.

To add fractions, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we can convert both fractions to have a denominator of 12.

1/4 is equivalent to 3/12, and 2/3 is equivalent to 8/12.

Now, we can add the fractions: 3/12 + 8/12 = 11/12.

Therefore, Jana has completed 11/12 or 11 out of 12 of her homework so far.

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