A grandfather's age in years is the same as his granddaughter's age in months. Together, they are 91 years old. How old is the grandfather?

Hello there! :)

Answer:

D. [tex](\frac{3 }{2}, 2)[/tex]

Step-by-step explanation:

Use the midpoint formula to solve:

[tex](x_{m}, y_{m} ) = (\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2}}{2})[/tex]

Plug in the points shown:

[tex](\frac{0+3 }{2}, \frac{4+0}{2})[/tex]

Simplify:

Midpoint coordinates at [tex](\frac{3 }{2}, 2)[/tex]

Answer:

[tex]y^{ \frac{3}{2}}[/tex]

Step-by-step explanation:

From the question posted, you've already initiated the solution but you applied a wrong approach;

Given

[tex]y^{\frac{4}{3}} . y^{\frac{2}{3} - \frac{1}{2}}[/tex]

Required

Simplify; using power property

Power property states that;

[tex]a^m.a^n = a^{m+n}[/tex]

[tex]a^m/a^n = a^{m-n}[/tex]

By comparison; we have to apply the first property;

This is shown below;

[tex]y^{\frac{4}{3}+\frac{2}{3} - \frac{1}{2}}[/tex]

Add fraction of the same numerator

[tex]y^{\frac{4+2}{3} - \frac{1}{2}}[/tex]

[tex]y^{\frac{6}{3} - \frac{1}{2}}[/tex]

[tex]y^{2 - \frac{1}{2}}[/tex]

Subtract fraction

[tex]y^{ \frac{4-1}{2}}[/tex]

[tex]y^{ \frac{3}{2}}[/tex]

The expression [tex]y^{\frac{4}{3}} . y^{\frac{2}{3} - \frac{1}{2}}[/tex] is equivalent to [tex]y^{ \frac{3}{2}}[/tex]

Answer:

C- 1/y

Step-by-step explanation:

go it right on edge

Answer:

1 hour and 6 minutes

Step-by-step explanation:

The next proportion must be satisfied:

18 °F / 28 °F = 2 hours / x hours

x = 2*28/18

x = 3.1 hours in total

Given that she has already waited 2 hours, she must wait 3.1 - 2 = 1.1 extra hours. 1 hour is equivalent to 60 minutes, then 0.1 hours is equivalent to 0.1*60 = 6 minutes.

Answer:

Answer is x= 15

Step-by-step explanation:

(3x+18)+(8x-3)=180

11x+15=180

11x=165

x=15

Answer:

x=15 degrees

Step-by-step explanation:

The given triangle is isosceles, so both base angles are both (3x+18).

We also know that angles on a line add up to 180 degrees, so

(3x+18) + (8x-3) = 180 degrees

Simplify

11x + 15 = 180 degrees

11x = 180-15 = 165

Divide by coefficient on left-hand side

x = 165/11 = 15 degrees.

Answer:

Left, Up

Step-by-step explanation:

Since -2 is to the left of 0 on the x-axis, we are moving left 2 units.

Since 7 is above 0 on the y-axis, we are moving up 7 units.

Answer:

The point (-2, 7) is graphed on a coordinate plane. The point is located 2 units left of the origin and 7 units up the origin 1st Blank

Step-by-step explanation:

Question formulation: A boy has a bag of red and blue PET caps, 60 red caps and 40 blue caps, which amount to a total of 100 caps. what is the ratio of the red caps to the total caps in the bag?

Answer

Given

red caps= 60

blue caps= 40

total caps= 60+40= 100

ratio of red to total caps= red:total = 60:100

= 60/100= 6/10

= 6:10

Answer:

(0,10)

Step-by-step explanation:

Answer:

[tex]g(x)=-(x+1)^2-4[/tex].

Step-by-step explanation:

The parent function is

[tex]f(x)=x^2[/tex]

Step 1: Start with the equation [tex]f(x)=x^2[/tex]. Write the equation for the graph of g(x) that has been

reflected, or flipped, over the x-axis.

[tex]f_1(x)=-f(x)[/tex]

[tex]f_1(x)=-x^2[/tex]

Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has

also been shifted down 4 units.

[tex]f_2(x)=f_1(x)-4[/tex]

[tex]f_2(x)=-x^2-4[/tex]

Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has

also been shifted left 1 unit.

[tex]g(x)=f_2(x+1)[/tex]

[tex]g(x)=-(x+1)^2-4[/tex]

Therefore, the required equation is [tex]g(x)=-(x+1)^2-4[/tex].

Answer:

.33 as a decimal or 33%

Step-by-step explanation:

Divide 1/3 and get .33 as your decimal. To convert to a percentage multiply your decimal by 100. (.33 x 100 = 33 )

Answer:

69

Step-by-step explanation:

Answer: (L. W)(x) = 16x^3 - 8x^2 + 2x

Step-by-step explanation:

The Area of a rectangle is calculated thus:

Area (A) = Width(W) × Length(L)

Given that:

Length = L(x) = 2x

Width = W(x) = 8x2 − 4x + 1

A = L(x) * W(x) = (2x) * (8x2 − 4x + 1)

Factorizing L(x) * W(x)

L(x) * W(x) = (L . W)(x)

(L . W)(x) = (2x) * (8x2 − 4x + 1)

(L . W)(x) = 16x^3 - 8x^2 + 2x

Answer:

I'd think the first one would be correct. To determine whether or not athletes have an increase in vertical leap when wearing the shoes.

I'm not totally sure but this answer just seems the most correct. It would prove if the manufacturers clam is valid. You would have to other brand and models of shoes. You would also have to test the same kind of shoes ie, gym shoe vrs gym shoe instead of gym shoe vrs flip flop.

You would also have to use the different shoe on the same test group of users/athletes to keep a constant.

Hope I help.

Answer:

5^5

Step-by-step explanation:

Answer:

A. c (in $) = 110(8) +175

Step-by-step explanation:

$175 is the starting price so in terms of an equation or an equation of a line it is the "b" or y-intercept.

c is the "y" or the depedent variable to solve for.

$110 is the increasing interval that is multiplied by the known variable, "x".

8 is the second variable, "x" but is known.

Answer:

A.

Step-by-step explanation:

The value of y will be 90°. The sum of angle of the two right angle is 180°. The property of the adjacent angle is used.

We do same operations on both the sides so that equality of both expressions doesn't get disturbed.

Solving equations generally means finding the values of the variables used in it for which the considered equation is true.

Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are an infinite number of solutions.

The angles subtended by a circle is 360°, then;

The equation is found as;

[tex]\rm 40^0+50^0+x+y+z=360^0 \\\\ x+y+z=270^0[/tex]

The sum of angle of the two right angle is 180°;

x°+40°+50°=180°

x=90°

y+50°+40°=180°

Y=90°

Hence, the value of y will be 90°.

Learn more about solving equations here:

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Answer:

2. 4t

3. 6 + n

4. 6w

5. d - 7

6. 62 + h

7. 20 - y

8. z/4

9. 20 - s

10. 3/5

11. 4s

12. u + v

**essentially in all these problems you have to determine the operation that fits each scenario and identify the constant vs. the unknown value. The unknown value is represented by a variable (a, x, y, z, t, d, etc.) and the constant is the given number.**

2. if you buy four packs of pencil with an unknown but same amount in each pack, then you have 4t. 4 TIMES the unknown amount equals the total.

3. you start with 6, your constant and then you ADD the number of pens your friend gave, but you don't know so you replace with the stated variable, n. 6 + n is the answer.

4. Each bag has six apples but you don't know how many bags you bought so if we replace this with the variable w. 6w (the constant always comes before the variable even though w6 = 6w) For example if you bought 2 bags, 6 x 2 = 12, a total of 12 apples.

5.  you start with chocolates, but we don't know the number. you eat seven of them, that means from the total number we are "missing" seven. therefore d - 7 accurately describes the scenario.

6. the constant is 62, and we are increasing by something, but we don't know what it is: 62 + h

7. we start with 20 balloons, then we lose an unknown number: 20 - y. We have to SUBTRACT from the total because we "lost".

8. we have an unknown number of fish in an aquarium but we are sure that 1/4 OF that number make up the angelfish population. The word "of" means multiply in mathematical terms so z • 1/4 OR z/4.

9. we have 20 marbles total. out of that number an unknown but represented value are red, "s". the rest are blue. So we will imaginarily take out all the red marbles. This action is SUBTRACTING "s" from 20 and we have only ___ amount of blue marbles left. Therefore the answer is 20 - s.

10. 2/5 OF the class are boys. The remainder are girls. What is 5/5 - 2/5? 3/5. This is the TRICK QUESTION!!

11. A car has 4 wheels each therefore 4 TIMES the total number of cars is the right equation. 4s.

12. If you start with an unknown amount of toys, "u", and you get an unknown amount more, "v", you are adding to your collection therefore the answer is u + v.

Hope these explanations help! There really isn't much more to the concept.

Step-by-step explanation:

Given.

[tex]3x+5y=3[/tex]

[tex]x+2y=0[/tex]

Take the second equation and subtract 2y to both sides.

[tex](x+2y)-2y=0-2y[/tex]

[tex]x=-2y[/tex]

Substitute x into the first equation and simplify.

[tex]3x+5y=3[/tex]

[tex]3(-2y)+5y=3[/tex]

[tex]-6y+5y=3[/tex]

[tex]-y=3[/tex]

Invert.

[tex]y=-3[/tex]

Substitute Y into your second equation.

[tex]x+2y=0[/tex]

[tex]x+2(-3)=0[/tex]

[tex]x-6=0[/tex]

Add -6 to both sides.

[tex](x-6)+6=0+6[/tex]

[tex]x=6[/tex]

Answer:

(6, -3)

Answer:

(6,-3)

Step-by-step explanation:

Got it right on the test

Hope this helps :)

Answer:

You have 9 red marbles, 21 green marbles, and 31 blue marbles.

Step-by-step explanation:

Let r equal the number of red marbles

Let b equal the number of blue marbles

Let g equal the number of green marbles.

"I have 5 less blue marbles than 4 times the red marbles."

4r-5=b

"I have 3 more green marbles than 2 times the number of red marbles."

2r+3=g

" All together I have 61 marbles."

r+b+g=61

Substitute the b and g for 4r-5 and 2r+3

r+(4r-5)+(2r+3)=61

5r-5+2r+3=61

5r+2r-5+3=61

7r-2=61

7r=63

r=9

2r+3=g

2(9)+3=g

21=g

4r-5=b

4(9)-5=b

36-5=b

b=31

You have 9 red marbles, 21 green marbles, and 31 blue marbles.

Let me know if this helps :)

Answer:

There are 9 red, 21 greens and 31 blues

Step-by-step explanation:

Set up equations

Let

R=# red

G=# green

B=# blue

I have 5 less blue marbles than 4 times the red marbles.

B=4R-5 .............(1)

I have 3 more green marbles than 2 times the number of red marbles.

G=2R+3..............(2)

All together I have 61 marbles.

R+G+B=61 ..................(3)

Solution:

substitute (1) & (2) in (3)

R + 2R+3 + 4R-5 = 61

Simplify

7R = 61+2 = 63

R = 63/7 = 9 ..........(4)

Substitute (4) in (1)

B = 4R-5 = 4(9) - 5 = 36-5 = 31

Substitute (4) in (2)

G = 2R+3 = 2(9) + 3 = 18+3 = 21

Answer:

B

Step-by-step explanation:

I remember when I had this question

Answer:

Let x represent the number of minutes.

Lets y represents the number of beats.

Now consider the graph, when the time is equal to 1 min, the total beats are 60. We can say that this point can be taken in a coordinate plane as (1,60).

Similarly, when time is equal to 2 mins, total beats are 120, and when time is equal to 3 mins, total beats are equal to 180 mins. So the these points on the coordinate plane can be represented as (2,120) and (3,180)

Plot all the three points, and draw a line which joins them and extend the line. The line shows the proportionality relation between both values

Answer:

0,0    1,60

Step-by-step explanation:

x=1

y=60

graph

Answer:

a - 8b + 13c

Step-by-step explanation:

a - (4b -( a - 5b + c + 3c -(a - b - 9c)))

a - (4b - (-5b + c + 3c + b + 9c)))

a - (4b - (-4b + 13c)))

a - (4b  + 4b - 13c)

a- (8b - 13c)

Answer:

30

Step-by-step explanation:

We know that BD = 20 + 5 = 25. Let's call the point where BD and CE intersect point A. Therefore, ΔBAC ≅ ΔBAE by HL (BC = BE = 25 because they are radii, BA and AB are congruent because of the reflexive property). We can use Pythagorean Theorem to find CA. We can write CA² + 20² = 25² so CA = 15 and since CA = AE = 15 and CE = CA + CE, CE = 15 + 15 = 30.

Answer:

Step-by-step explanation:

BE=BC=25 in

trg BCE isosceles so CE=2✓25^2-20^2

=2"✓625-400=2*✓225=2*15

CE=30

Answer:

n^2/(n + 5)

Step-by-step explanation:

The numerators are 1^2, 2^2, 3^2, 4^2, etc.

The denominators are 6, 7, 8, 9, etc.

The nth numerator is n^2.

The nth denominator is n + 5.

Answer: n^2/(n + 5)

The range of the curve is from -6 to 10, i.e. -6 ≤ y ≤ 10.

Given is a graph of a curve having endpoints at (-10, -6) and (0, 10), we need to find its range.

To find the range of a curve, we need to determine the set of all possible y-values that the curve can attain.

In this case, we have the endpoints of the curve as (-10, -6) and (0, 10).

The range of the curve is the set of all possible y-values. To find it, we need to identify the minimum and maximum y-values.

The minimum y-value can be found at the lowest point of the curve. From the given endpoints, we can see that the lowest point lies at (-10, -6).

The maximum y-value can be found at the highest point of the curve. From the given endpoints, we can see that the highest point lies at (0, 10).

Therefore, the range of the curve is from -6 to 10, inclusive: [-6, 10].

Learn more about range click;

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Answer:

-6x -8

Step-by-step explanation:

7-3(2x+5)

Distribute

7 - 6x -15

Combine like terms

-6x +7-15

-6x -8

Answer:

[tex]\boxed{\sf \ \ \ -6x - 8 \ \ \ }[/tex]

Step-by-step explanation:

Hello

7 - 3(2x+5) = 7 -3*2x -3*5 = 7 - 6x - 15 = -6x - 8

hope this helps

do not hesitate if you have any question

Answer:

A: the graph is decreasing

The graph is decreasing because the slope is negative. Then the correct option is A.

If the value of y increases as the value of x increases, then increasing function.

And if the value of y decreases as the value of x increases, then decreasing function.

In the graph, as the value of x increases, the value of y decreases.

The graph is decreasing because the slope is negative.

Then the correct option is A.

More about the increasing and decreasing of function link is given below.

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Answer: 0.000000002

Step-by-step explanation:

Evaluation of (2x10^-3)^3 will be achieved by using the law of indices or exponent.

(A^x)^y = A^xy

Therefore,

(2x10^-3)^3= 2x10^-9

Convert the number in standard form back to normal number form

2×10^-9 = 0.000000002

Therefore,

(2x10^-3)^3 = 0.000000002

Answer:

Solution,

[tex]6.2(a + 5) - 2a + 1.2 \\ = 6.2 \times a + 6.2 \times 5 - 2a + 1.2 \\ = 6.2a + 31 - 2a + 1.2 \\ = 6.2a - 2a + 31 + 1.2 \\ = 4.2a + 32.2[/tex]

Hope this helps.

Good luck on your assignment...