Question 4
At practice, Diego does twice as many push-ups as
Noah, and also 40 jumping jacks. He does 62 exercises
in total. The equation 2x+40=62 describes this situation.
What does the variable x represent?
The number of push-ups Diego does.
The number of push-ups Noah does.
The number of jumping jacks Diego does.
The number of jumping jacks Noah does.

Answer:

y = 4x + 1

Step-by-step explanation:

y = mx + b

The line goes thru (0, 1) and (1, 5)

The slope = m = (5 - 1)/ 1 - 0) = 4/1 = 4

The y-intercept is (0, 1), so b = 1

y = 4x + 1 is the equation of the line

Given:

[tex]x=-\dfrac{8}{9},\ y=-\dfrac{3}{5}[/tex]

To verify:

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

Solution:

We need to verify,

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

Taking left hand side, we get

[tex]LHS=x+y[/tex]

After substituting the values, we get

[tex]LHS=-\dfrac{8}{9}+\left(-\dfrac{3}{5}\right)[/tex]

[tex]LHS=-\dfrac{8}{9}-\dfrac{3}{5}[/tex]

[tex]LHS=\dfrac{-40-27}{45}[/tex]

[tex]LHS=\dfrac{-67}{45}[/tex]

Now,

Taking right hand side, we get

[tex]RHS=y+x[/tex]

After substituting the values, we get

[tex]RHS=-\dfrac{3}{5}+\left(-\dfrac{8}{9}\right)[/tex]

[tex]RHS=-\dfrac{3}{5}-\dfrac{8}{9}[/tex]

[tex]RHS=\dfrac{-27-40}{45}[/tex]

[tex]RHS=\dfrac{-67}{45}[/tex]

Clearly,

[tex]LHS=RHS[/tex]

Hence verified.

Answer:

$830

Step-by-step explanation:

x/2=200+215

x/2=415    multiply by two on both sides to get x alone

x=830

Answer:

The question has a picture attached of both rectangular prisms which I have attached and solved.

Answer:   1320 cm³

Step-by-step explanation:  

top prism = 5×12×10=600  

lower prism = 15×12×(15-10) = 720

Adding both volumes

720 + 600 = 1320 cm³

Answer:

$699.98

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Number of students = number of students that went to the museum / percentage of students that went to the museum

90 / 0.45 = 200 students

Answer:

132 degrees

Step-by-step explanation:

To solve this problem, you need to know a couple of rules

1) Inscribed angle theroem: when an angle is inscribed in a circle and touches the other end (as opposed to ending at the diameter of the circle), the measure of this angle is half of the measure of the arc.

2)Angles of a quadrilateral shape add up to 360 degrees.

3) The angles inside a circle and the angles of the circles arclength adds up to 360 degrees.

So first, solve angle S with inscribed angle theorem. 126/2 = 63

Then, use the rule that all arc angles in a circle add up to 360 degrees to find the arc angle from Q to S. 360-90-126 = 144. Now find angle P with inscribed angle theorem by doing 144/2 = 72.

Now, use the rule that all angles in a quadrilateral add up to 360 to find R. 360-93-72-63 = 132.  

Let me know if this doesn't work, I'll look at it again.

Answer:

rational

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

Answer:

the dimension of the rectangle is 4 cm and 6 cm respectively

Step-by-step explanation:

The computation of the dimension of the rectangle is shown below:

Given that

The perimeter of the rectangle is 20 cm

The width be x

So, the length would be 2 1 ÷ 4 x - 3 i.e.  9 ÷ 4x - 3

Now as we know that

Perimeter of the rectangle = 2 (length + width)

20 = 2 (9 ÷ 4x - 3 + x)

20 = 9 ÷ 2x - 6 + 2x

20 = 4.5x - 6 + 2x

26 = 6.5x

x = 4 cm

Now the length would be

= 9 × 4  ÷ 4  - 3

= 6 cm

Hence, the dimension of the rectangle is 4 cm and 6 cm respectively

Answer:

2x=80°

x=40°

40°+20°=60°

Step-by-step explanation:

all triangles are 180°

Answer:

The probability that the red die shows a six or the green die shows a six is 1136 .

Answer:

R = 23 ohms

Step-by-step explanation:

Start with V = I*R.  Solve for R:  R = V/I

Here I = 8 amps and V = 184 volts, and so

R  = (184 volts) / (8 amps) = 23 ohms

Answer:

lets go

Step-by-step explanation:

YAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAY

Step-by-step explanation:

As,

x + 14 + 3x = 90 [Complementary Angles]

=> 4x = 90 - 14

=> 4x = 76

[tex] = > x = \frac{76}{4} [/tex]

=> x = 19

Hence,

<1 = x + 14°

= 19 + 14 = 33°

<2 = 3x

= 3 × 19° = 57°

Answer:

14/20 or simplified 7/10 it can also be shown as 70% or 0.7 or 0.70

Step-by-step explanation:

its the second option because it is clearly shown and described on the screen

Answer:A

Step-by-step explanation: im not too sure but i think 1-2/5=3/5 which would be red so

Answer:

The answer to this is a because it has a sequence of three

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{(-2^3)(3^2)}{6}+(-2^2)(3^2)}[/tex]

[tex]\mathsf{(-2)^3=\bf -8}[/tex]

[tex]\mathsf{= \dfrac{-8(3^2)}{6}+(-2^2)(3^2)}[/tex]

[tex]\mathsf{3^2=\bf 9}[/tex]

[tex]\mathsf{= \dfrac{(-8)(9)}{6}+(-2^2)(3^2)}[/tex]

[tex]\mathsf{-8(9)= \bf -72}[/tex]

[tex]\mathsf{= \dfrac{-72}{6}+(-2^2)+(3^2)}[/tex]

[tex]\mathsf{\dfrac{-72}{6}=\bf -12}[/tex]

[tex]\mathsf{= -12+(-2)^2(3^2)}[/tex]

[tex]\mathsf{-2^2=\bf 4}[/tex]

[tex]\mathsf{= -12+4(3^2)}[/tex]

[tex]\mathsf{3^2=\bf 9}[/tex]

[tex]\mathsf{= -12+4(9)}[/tex]

[tex]\mathsf{4(9)= \bf 36}[/tex]

[tex]\mathsf{-12 + 36 = \bf 24}[/tex]

[tex]\boxed{\boxed{\large\text{Answer: \huge\bf Option C. 24}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

[tex]108 in^{2}[/tex]

Step-by-step explanation:

Separate it into 2 parts:

The first would be that the length and width of the smaller rectangle would be, 7 in. and 6 in.

7 x 6 = 42 in^2

The second would be that the length and width of the larger rectangle would be, 11 in. and 6 in.

11 x 6 = 66 in^2

Total:

66 + 42 = 108 in^2

Answer:

108 [tex]in ^2[/tex]

Step-by-step explanation:

This polygon consists of two rectangles, one in the top-right hand corner and another in the bottom. To divide these two rectangles, imagine a line extended from the central horizontal line in the polygon. As I work the problem, remember that the formula for the area of a rectangle is [tex]A=l * h[/tex], where A is the area of the rectangle, l the length of the rectangle (one of the sides), and h is the height of the rectangle (the length of a side perpendicular to l).

Starting with the top-right rectangle:

We already know one of the sides of the rectangle is 4 in, so let's imagine this to be h, because it is the height of the rectangle. Finding l is more complicated. We know the length of the larger rectangle is 12 in (more on that later) and the 6 in length is the part of the length that is not a part of the top-right rectangle. This, since the vertical line all the way to the right is straight, the length is the difference between these two lengths, or:

[tex]l=12-6=6[/tex] in

Now that we know l and h, we can evaluate the area of the first rectangle, which is

[tex]A= 6 *4= 24[/tex] in^2

Now for the bottom rectangle:

We know both l and h for this rectangle, which are 12 in and 7 in respectively. Using the area formula for a rectangle above:

[tex]A=12*7=84[/tex] in^2

Since the polygon contains both rectangles, its area is the sum of the areas of the two rectangles. Thus,

[tex]A=24+84=108[/tex] in^2

QED

Answer:

46

Step-by-step explanation:

I think the answer Is 46 I'm not 100% sure though but I do think it is 46

Answer:

∠HGJ + ∠KJG = 180°

So, ∠KJG = 62°

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]A=(3+8)\cdot4+\frac12\cdot3\cdot2+\frac12\cdot3\cdot3=44+3+4,5=51.5\,ft[/tex]

Answer:

x = [tex]-\frac{1}{3}[/tex], y = 2

Step-by-step explanation:

3x + 3y - 7 = 12x + y

6y - 12x - 1 = -45x

(3x - 12x) + (3y - y) = 7

(-12x + 45x) + 6y = 1

-3(-9x + 2y = 7)

33x + 6y = 1

27x - 6y = -21

33x + 6y = 1

60x = -20 -> x = -20/60 = -1/3

-9x + 2y = 7 -> y = [tex]\frac{7+9x}{2}[/tex] = [tex]\frac{7+9*-\frac{1}{3}}{2}[/tex] = 2

Answer:

no.both are equal.

Step-by-step explanation:

72 km/h=72000/(60×60)=20m/s

Answer:

They are equal

Step-by-step explanation:

72 Kilometers per Hour equals the same as 20 Meters per Second.