Please help me answer both questions if they are correct I’ll give brainliest

Let the costs of shoes, t-shirt, and glasses be represented by s, t, g, respectively. The problem statement tells us these relationships:

... s = 2t

... g = t/2

... s +t +g +9 = 65 . . . . . the $9 cost of the hat is added into the total

_____

Solution

Substituting for s and g, we have ...

... 2t +t +t/2 +9 = 65

... (3 1/2)t = 56 . . . . . collect terms

... t = 56/3.5 = 16 . . . . divide by the coefficient of t

The shoes are 2t, so $32.

The t-shirt is t, so $16.

The sunglasses are t/2, so $8.

The hat is $9.

Answer:

[tex]y=\frac{3w}{10\left(2w-1\right)}[/tex]

Step-by-step explanation:

We are given

Miss Teng normal walk:

speed =0.5 m/s

distance traveled =y km =y*1000

now, we can find time

we know

time = distance / speed

[tex]t_1=\frac{1000y}{0.5}[/tex]

[tex]t_1=2000y[/tex]

Miss Teng  walk on cloudy day:

speed =w m/s

distance traveled =y km =y*1000

now, we can find time

we know

time = distance / speed

[tex]t_2=\frac{1000y}{w}[/tex]

If she reached her school 5 minutes earlier than usual

so,

[tex]t_1-t_2=5\times 60 sec[/tex]

[tex]t_1-t_2=300[/tex]

now, we can plug values

[tex]2000y-\frac{1000y}{w}=300[/tex]

now, we can solve for y

we can multiply both sides by w

[tex]2000yw-\frac{1000y}{w}w=300w[/tex]

[tex]2000wy-1000y=300w[/tex]

[tex]1000y\left(2w-1\right)=300w[/tex]

[tex]y=\frac{3w}{10\left(2w-1\right)}[/tex]

Answer:

5 years.

Step-by-step explanation:

She earns $339.3 per year on interest rate. So I divided 1,696.50 by 339.3 to get the amount of ears.

Lina invested for 5 years.

According to the problem,

So, we can say $ 1,696.50 is the interest

∴ Prt = 1696.50

⇒ (7800)(4.35/100)t = 1696.50

⇒ t = 5

∴ Line invested for 5 years.

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Answer:

(21,5)

Step-by-step explanation:

To find the slope that passes through the points (7,5) and (21,15) , we use the formula

m = (y2-y1)/ (x2-x1)

   = (15-5)/(21-7)

   = 10/14

  =5/7

We want a slope that is 1/3 this slope so we will multiply by 1/3

5/7 * 1/3= 5/21

We know the slope and one point (0,0)  we can use the same formula to figure out x and y

m = (y2-y1)/ (x2-x1)

5/21 = (y2-0)/ (x2-0)

Let the tops be equal and the bottoms be equal

5 = y2-0

5 =y2

and the bottoms

21 = x2-0

21= x2

We have the point

(21,5)

Answer:

here you go

View the picture for your answer!

have a wonderful day :))

Answer:

16(3x - 1)

Step-by-step explanation:

the greatest common factor of 48 and 16 is 16, hence

48x - 16 = 16(3x - 1)

Final answer:

After factoring out the greatest common factor of 16 from the expression 48x-16, the correct factored form is 16(3x - 1). The friend's factorization is correct if this result was obtained, demonstrating the universal application of mathematical rules.

Explanation:

To evaluate if your friend factored the expression 48x-16 correctly, we look for the greatest common factor that both terms in the expression share. Both 48x and 16 are divisible by 16. Factoring out the greatest common factor of 16, we get:

16(3x - 1)

This is the factored form of the expression 48x-16, which shows that your friend is correct if they arrived at this result. This method is an application of the distributive property, which states that a(b + c) = ab + ac. In this case, we take out a '16' from both terms, which is the inverse process - factoring.

Moreover, the principles that apply to factoring expressions are the same regardless of location or time, demonstrating the universality of mathematical rules. Whether we are factoring polynomials or checking arithmetic, using the correct rule and applying it properly is essential.

Answer:

a/b =6

Step-by-step explanation:

We want to evaluate a/b

a=24, b=4

Substitute these values into the expression

a/b =24/4

    = 6

Final answer:

When evaluating the expression a/b with a=24 and b=4, the result is 6, as you simply divide 24 by 4.

Explanation:

The expression to evaluate is a/b, where a=24 and b=4.

To calculate this, simply divide the value of a by the value of b:

Step-by-step calculation:

Insert the known values into the expression: a/b = 24/4.

Divide 24 by 4 to get the result.

24 divided by 4 equals 6.

Therefore, if a=24 and b=4, the value of a/b is 6.

[tex]n,\ n+1-\text{ two consecutive whole numbers}\\57-\text{the sum}\\\\n+n+1=57\qquad\text{subtract 1 from both sides}\\2n=56\qquad\text{divide both sides by 2}\\n=28\\\\n+1=28+1=29\\\\Answer:\ \boxed{\text{The greater of the two numbers is 29}}[/tex]

The two consecutive whole numbers that sum to 57 are 28 and 29. The solution was achieved by setting up an equation and solving for x which represents the smaller number. The greater number is 29.

The sum of two consecutive whole numbers is 57 pertains to a simple arithmetic problem. If two consecutive numbers sum to 57, we can set up an equation to solve for the numbers. Let's call the smaller number 'x'. This means the next number would be 'x + 1' since it's consecutive, or next in line. The equation for your problem would then be x + (x + 1) = 57. Simplifying the equation gives us 2x + 1 = 57, and then subtracts 1 from both sides to get 2x = 56.

The last step is to divide both sides by 2, which gives us: x = 28. So, the smaller number is 28 and the greater number is 29.

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Answer:

[tex]y-6=5(x-1)[/tex]

Step-by-step explanation:

To make the line parallel, it has to have the same slope as the other. Because it is in slope-intercept form, we can see that the slope of the line is 5.

Now we have all of the numbers we need for point-slope form. The point-slope form looks like this:

[tex]y-y_{1}=m(x-x_{1})[/tex]

So when we input our values for the variables, the equation is:

[tex]y-6=5(x-1)[/tex]

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (relevant later)

Point-slope form:

y - y₁ = m(x - x₁)        "m" is the slope

For lines to be parallel, their slopes have to be the SAME

The given line's slope is 5, so the parallel line's slope is also 5.

So you know:

m = 5

(x₁ , y₁) = (1 , 6)

Now you can plug this in:

y - y₁ = m(x - x₁)  

y - 6 = 5(x - 1)

Answer:

value of QZ = 8 units and QM =  12 units.

Step-by-step explanation:

Given: In triangle PQR has medians QM and PN that intersect at Z.

If ZM = 4 units.

In the figure given below;  second median divided the two triangles formed by the first median in the ratio 2:1.

We have to find the value of QZ and QM;

QZ:ZM = 2: 1

⇒ [tex]\frac{QZ}{ZM} = \frac{2}{1}[/tex]

Substitute the value of ZM =4 units and solve for QZ;

[tex]\frac{QZ}{4} = \frac{2}{1}[/tex]

Multiply both sides by 4 we get;

[tex]QZ = 2 \times 4 = 8 units[/tex]

Now, calculate QM;

QM = QZ+ZM = 8 + 4 = 12 units.

Therefore, the value of QZ and QM are; 8 units and 12 units

Answer:

640 bacteria.

Step-by-step explanation:

Make a chart.

Bacteria    Weeks

40                  0

80                  1

160                  2

320                 3

640                 4

It starts off with 40 bacteria, which means no weeks have passed so far. That is why 40 pairs with 0 rather than 1.

Answer:363

Step-by-step explanation:

We have to find partial sum for the sequence 243 , 81 , 27 ..... up to 5 terms(S5 given)

The sequence actually is 3^5,3^4.,3^3.....

Therefore first 5 terms are 1) 3^5 I.e. 243

2) 3^4 I.e. 81

3) 3^3 I.e. 27

4)) 3^2 I.e. 9

5) 3^1 I.e. 3

Adding all those no. we get partial sum of first 5 no. of the sequence

So, 243 + 81 + 27 + 9 + 3

= 363

Hope it helps!!!

Answer:

D. 363 is the one

The domain is the set of all numbers. The range is also the set of all real numbers.

Why is this the case? Because the line extends forever in both directions along the x and y axis. We can plug in any x value and solve for y, or vice versa, and we don't have any restrictions for the input or output.

-----------------------

To write "the set of all real numbers" in interval notation, you would write [tex](-\infty, \infty)[/tex]

This is the interval from negative infinity to positive infinity, spanning the entire real number line.

Answer:

the probability of getting the exact coins that make $0.15 is 33.3% (1/3)

Step-by-step explanation:

Answer:

2A /b = h

Step-by-step explanation:

A=1/2 bh

We want to isolate h

First we multiply by 2

2A = 2 * 1/2 bh

2A = bh

Then we divide by b to isolate h

2A /b = bh/b

2A /b = h

Answer:

1. ∠LOQ = 80°

2. ∠LRQ = 40°

3. ∠LBQ = 40°

Step-by-step explanation:

It is given that ARC QL has a measure of 80.

1.

m∠LOQ: ∠LOQ is the central angle from ARC QL so it has SAME MEASURE.

∠LOQ = 80°

2.

m∠LRQ: ∠LRQ is the opposite angle from ARC QL so it is HALF of ARC QL.

∠LRQ = [tex]\frac{1}{2}(80)=40[/tex]

∠LRQ = 40°

3.

m∠LBQ: ∠LBQ is also another opposite angle from ARC QL so it is HALF of ARC QL as well.

∠LBQ = [tex]\frac{1}{2}(80)=40[/tex]

∠LBQ = 40°

Answer:

C

Step-by-step explanation:

$4.50 x 4 = $18.00          $6.00 x 2 = $12.00          $18 + $12  = $30

$4.50 + $6.00 = $10.50

Answer:

38.94

Step-by-step explanation:

To find the area, multiply the length times the width. In this case 9.5 times 4.1.

Answer:

changing by one

Step-by-step explanation:

The vertex of the parabola y = (x – 5)² + 8 with a vertical axis of symmetry is the point (5, 8).

The question is asking for the vertex of the parabola y = (x − 5)² + 8 which has a vertical axis of symmetry. In the general equation for a parabola, y - k = a(x - h)², the vertex is denoted by the (h, k). So, comparing this with the given parabola equation, we can determine that the h value corresponds to the value inside the brackets in the (x – h)² part of the equation, and the k value corresponds to the term added or subtracted outside the squared term.

For the given equation, y = (x – 5)² + 8, we can see that h = 5 and k = 8. Therefore, the vertex of the parabola is at the point (5, 8).

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Answer: 7/16 or .4375

Step-by-step explanation: 1/4 of 1 is 1/4. 1/4 of 3/4 is .1875 which also equals 3/16. Add 1/4 and 3/16 to get 7/16 cups of sugar or 0.4375. Hope this helps!

The x-intercept is for y = 0.

substitute y = 0 to the equation of the function:

[tex]\dfrac{1}{3}x+y=-15\\\\\dfrac{1}{3}x+0=-15\\\\\dfrac{1}{3}x=-15\qquad\text{multiply both sides by 3}\\\\\boxed{x=-45}[/tex]

Answer:

(-45,0)

Step-by-step explanation:

I took the test

Answer:

The area is 1/2×3×3= 4.5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

given y = 3(x + 2)(x - 2) = 3(x² - 4) = 3x² - 12

for the y- intercept let x = 0

f(0) = - 12 → y-intercept is the point (0, - 12) → True

for x-intercepts let y = 0

3(x + 2)(x - 2) = 0

x + 2 = 0 ⇒ x = - 2

x - 2 = 0 ⇒ x = 2

x- intercepts are (- 2, 0) and (2, 0) → not (0, - 12)

since f(x) = 3x² - 12 is symmetric about the y-axis

the vertex is at (0, - 12 ) → not (- 2, 2)

Final answer:

To calculate the total distance traveled by the ball in the first four seconds, we sum the distances for each second, yielding 13k feet.

Explanation:

The student has provided a sequence of distances that a ball rolls down an inclined plane, with distances increasing each second. The distances in successive seconds are given by k feet, 2.5k feet, 4k feet, and so on. To calculate the total distance traveled by the ball in the first four seconds, we use the arithmetic sequence formula.

Let's calculate the distance for each second:

1st second: k feet

2nd second: 2.5k feet

3rd second: 4k feet

4th second: By the same pattern it follows that the 4th second should cover 5.5k feet.

To find the total distance, we sum these values:

Total distance = k + 2.5k + 4k + 5.5k = 13k feet.

This is the total distance traveled by the ball in the first four seconds.

Answer:

Step-by-step explanation:

We can set up an equation:

4(3x+4)=76

We can distribute the left side and get:

12x+16=76

Subtract 16 from both sides:

12x=60

Divide 12 from both sides:

x=5

Check:

4(3*5+4)

4(15+4)

4(18)

76

So x=5

Answer:

t > - 27

Step-by-step explanation:

t + 4 > 31.  Next, solve for t:  t > -27

Answer:

t+4 > 31

t > 27

Step-by-step explanation:

(t + 4) exceeds 31

t+4 > 31

Subtract 4 from each side

t+4-4 > 31-4

t > 27

Answer:

tn = a*2^(n - 1)

Step-by-step explanation:

a = 4

r = 2

tn= a*2^(n-1)

Try it

t3 = 4*2^(3 -1)        Combine the power

t3 = 4 * 2^2            Find 2^2

t3 = 4 * 4                Multiply

t3 = 16                     Answer for t3

Answer:

2^(n+1)

Step-by-step explanation:

You don't even need to use algebraic methods or the formula for this; it's just common sense. 4=2^2, 8=2^3, 16=2^4.

4 is the term 1

8 is term 2

2=term # (1) + 1 for 4

3 = term # (2) + 1 for 8

And so on

So it is 2 to the power of (term # + 1)

Answer:

300 dollars of interest

Step-by-step explanation:

5000 (0.06)

300

Answer:

$30

Step-by-step explanation:

You are being asked to figure out simple interest, I think.

Givens

Formula

i = P*r*t

Solution

Edit

You want this to be done using a % proportion. Is that correct from what I read in the comments after the question (which I didn't see -- sorry).

So it comes to the same thing.

Answer:

12

Step-by-step explanation:

Change the percentage into a decimal

30% = 30/100 = 0.30

Multiply 40 with 0.30

40 x 0.30 = 12

12 more people adopted, making 52 in all.

~

Answer:

52

Step-by-step explanation:

30% more means the original 100% plus 30% more of the original 40

That's 130% = 130/100 = 1.3

"of" means x, so it's 40 x 1.3 = 52 people

Triangles NPM and ABC are similar by SAS, establishing that angle ABC corresponds to angle NPM. Thus, <ABC = <MNP.

In triangles NPM and ABC, the given information suggests that these triangles are similar by the Side-Angle-Side (SAS) criterion. Specifically, MP = AC, AB = NM, and BC = PN, along with the corresponding equal angles A = M, B = N, and C = P.

The Angle-Angle Similarity Postulate asserts that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Therefore, triangles NPM and ABC are similar.

The corresponding angles in similar triangles are equal. Hence, angle ABC is equal to angle NPM. Therefore, the correct answer is:

<MNP

This is because angle ABC in triangle ABC corresponds to angle NPM in triangle NPM.