Jen is making a frame to stretch a canvas over for a painting. She nailed four pieces of wood together at what she believes will be the four vertices of a square. How can she be sure that the canvas will be a square?

a. All four of the pieces of wood are the same length & at least two interior angles are congruent.

b. At least two pieces of wood are the same length & at least two interior angles are congruent.

c. At least two pieces of wood are the same length & all four interior angles are congruent.

d. All four of the pieces of wood are the same length & all four interior angles are congruent.

The line y = 4x + 2 is graphed and attached with the answer.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written to express proportional relationship as -

y = kx  {k is constant}

We have a equation that represents a line as -

y = 4x + 2

We can graph the given equation as shown in the figure attached.

Therefore, the line y = 4x + 2 is graphed and attached with the answer.

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To round off or add zero to the calculated answer of 0.00001258 L and give a final answer with three significant figures, round up the last significant figure to 6.

In order to round off or add zero to the calculated answer and give a final answer with three significant figures, follow these steps:

To round off or add zero to the calculated answer to give a final answer with three significant figures, consider the following: For the value 0.00001258 L, the third significant figure is 5. Since the digit after the third significant figure (8) is greater than or equal to 5, we round up the third significant figure. Therefore, the final answer is 0.0000126 L.

To round off or add zero to the calculated answer to give a final answer with three significant figures, consider the following:

For the value 0.00001258 L, the third significant figure is 5. Since the digit after the third significant figure (8) is greater than or equal to 5, we round up the third significant figure. Therefore, the final answer is 0.0000126 L.

Final answer:

The system of equations 9x - 3y = 3 and 3x + 8y = -17 is solved using elimination. By multiplying the second equation by 3 and subtracting the first from the resulting equation, y is eliminated and found to be -2. Substituting y into one of the original equations then gives x as -1/3.

Explanation:

Solving a System of Equations by Elimination

To solve the system by elimination, we aim to eliminate one of the variables by combining the equations. We have the equations 9x - 3y = 3 and 3x + 8y = -17. Let's multiply the second equation by 3 to align the coefficients of x.

After multiplication, our system looks like this:

Now, subtract Equation 1 from Equation 2, which eliminates the x variable:

-3y - 24y = 3 - (-51)

-27y = 54

To find the value of y, divide both sides by -27:

y = -2

Now that we have y, we can substitute it back into one of the original equations to find x:

3x + 8(-2) = -17

3x - 16 = -17

3x = -1

x = -1/3

So the solution to the system is x = -1/3 and y = -2.

Answer:

kf(x)

Step-by-step explanation:

I got it right.

Answer:

the answer is a parabola

Answer:

46

Step-by-step explanation:

To subtract[tex]\(\frac{11}{12} - \frac{5}{8}\), find a common denominator (24), then subtract numerators: \(\frac{11}{12} - \frac{5}{8} = \frac{7}{24}\)[/tex] in simplest form.

To subtract the fractions [tex]\(\frac{11}{12} - \frac{5}{8}\[/tex]), we need to find a common denominator.

The least common multiple (LCM) of 12 and 8 is 24.

Now, rewrite both fractions with the denominator 24:

[tex]\[\frac{11}{12} \times \frac{2}{2} = \frac{22}{24}\]\[\frac{5}{8} \times \frac{3}{3} = \frac{15}{24}\][/tex]

Now, subtract:

[tex]\[\frac{22}{24} - \frac{15}{24} = \frac{22 - 15}{24} = \frac{7}{24}\]So, \(\frac{11}{12} - \frac{5}{8} = \frac{7}{24}\)[/tex]

Answer:

Paul is 70 kg, John is 62 kg and David is 65 kg.

Step-by-step explanation:

Let x the mass for each person.

Paul = x

John is lighter than Paul, so John = x-8

David's mass is 5 kg less than John's, so David = x-5

Solution:

Make an equation.

x + (x-8) + (x-5) = 197

3x -13 = 197

3x = 197 + 13

3x= 210, then divide both side by 3, to get 70.

Do substitution to get a correct answer.

70+62+65= 197

197= 197

Answer:

A

Step-by-step explanation:

The number of strawberries Sameer ate is 6.

Given that, Sameer ate a plum with 32 calories and several strawberries with 4 calories each. The total number of calories in Sameer’s snack was 56.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Now, remaining calories=Total number of calories - Number of calories in plum

=56-32=24

Number of strawberries=24/4 =6

Therefore, the number of strawberries Sameer ate is 6.

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To cover 348 tiles when one bottle can cover 20 tiles, you divide 348 by 20 which equals 17.4, and then round up to 18 bottles since you can't buy a fraction of a bottle.

To determine how many bottles of paint are needed to cover 348 tiles when one bottle covers 20 tiles, you should divide the total number of tiles by the number of tiles that can be covered by one bottle. The calculation is as follows:

Divide 348 (the total number of tiles) by 20 (the number of tiles one bottle of paint can cover).

348 \/ 20 = 17.4

Since you can't buy a fraction of a bottle, you would need to round up to the next whole number. Therefore, you need 18 bottles of paint to cover all 348 tiles.

Answer:

29

Step-by-step explanation:

29 is only divisible by 1 and itself.