Jake solved an equation, as shown
1. 1/3x + 7 = 15
2. 1/3x + 7 - 7 = 15
3. 1/3x = 15
4. 3 • 1/3x = 3 • 15
5. x = 45
Which statement is true?
Jake made a mistake in step two
Jake made a mistake in step four
Jake made a mistake in step five
Jake solved the equation correctly​

I assume the question is whether the vector b is a linear combination of v₁ and v₂. If it is, then that means there are scalars c₁ and c₂ such that

b = c₁ v₁ + c₂ v₂   ==>   (7, 4, -3) = c₁ (1, 2, -5) + c₂ (2, 5, 6)

This gives the system of equations,

c₁ + 2c₂ = 7

2c₁ + 5c₂ = 4

-5c₁ + 6c₂ = -3

which has no solution, since

-2 (c₁ + 2c₂) + (2c₁ + 5c₂) = -2(7) + 4   ==>   c₂ = -10

but substituting this into any two equations in the system gives contradictory results. For instance,

c₁ + 2c₂ = c₁ - 20 = 7   ==>   c₁ = 27

2c₁ + 5c₂ = 2c₁ - 50 = 4   ==>   c₁ = 27

-5c₁ + 6c₂ = -5c₁ - 60 = -3   ==>   c₁ = -57/5

This means that b is not a linear combination of v₁ and v₂.

Answer:

Width = 3.773 inches

Length = 79.227 inches-

Step-by-step explanation:

g = 7(3w)             Eq. 1

166 = 2(g+w)       Eq. 2

g = length

w = width

From Eq, 1:

g = 21w              Eq. 3

Replacing Eq. 3 in Eq. 2

166 = 2(21w + w)

166 = 2(22w)

166 = 44w

166/44 = w

w = 3.773

From Eq. 3

g = 21(3.773)

g = 79.227

Check:

From Eq. 2:

166 = 2(79.227 + 3.773) = 2 * 83

Answer:

equation which represent this situation is 30 - 13x/6 =4

Solution to this equation is x = 12

As we see that there is one equation and degree of x is one thus there is one solution.

Step-by-step explanation:

Total no. of chocolates with Jonathan = 30

 no. of chocolates given to David IS x

Given

He then gives Sarah half the number of chocolates that he gave David

no. of chocolates given to Sarah = 1/2 of no. of chocolates given to David

no. of chocolates given to Sarah = 1/2 of x = x/2

Again given

gives Lily two-thirds of what he gave David. After giving away the chocolates

no. of chocolates given to Lily = 2/3 of no. of chocolates given to David

no. of chocolates given to Lily = 2/3 of x = 2x/3

Total no. of chocolates given to David , Sarah and lily = x+x/2+2x/3

LCM of 2 and 3 is 6

Total no. of chocolates given to David , Sarah and lily =( 6x + 3x+ 4x)/6

Total no. of chocolates given to David , Sarah and lily =13x/6

Now, additional information in the problem is

After giving away the chocolates, Jonathan has 4 chocolates left

Chocolate left with Jonathan = Total no. of chocolates with Jonathan  - Total no. of chocolates given to David , Sarah and lily

4 = 30 - 13x/6

=> 4 + 13x/6  = 30

=> 13x/6 = 30-4 = 26

=> x = 26*6/13 = 2*6 =12

Thus, equation which represent this situation is 30 - 13x/6 =4

Solution to this equation is x = 12

As we see that there is one equation and degree of x is one thus there is one solution.

Answer:

1.5 * 7 that is the answer of the question

Answer:

2/5 remaining

Step-by-step explanation:

If a job is 35 and 3/5 was completed, 3/5 of 35 = 21

That is 35 - 21 = 14

The fraction of the job remaining to be done will then be 14/35 = 2/5

Answer:

D.

Hope this helps!

Step-by-step explanation:

A and C are both squares and B is a rectangle but is different because the values are in different spots than the on the solid figure shown.

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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The rate of interest is 73%.

What is the annual rate?

The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, mortgage loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.

Given that 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².

A dollar to triple in 2 years.

Thus putting X = 3 in X = (1+r) ²

3 = (1+r) ²

Take square root on both sides:

√3 = 1 + r

Subtract 1 from both sides:

r = √3 - 1

r = 0.73

r = 73%

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Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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Answer:

-18 and -27 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Answer:

-8x - 8

Step-by-step explanation:

You have to combine like term.

So you add 16x + -24x = -8x

And you add -12 + 4 = -8

Your answer would be -8x - 8

I hope this helps!

Answer:

area=28cm^2

Step-by-step explanation:

4×5=20

20÷2=10 area of the bigger triangle

4×2=8

8÷2=4 area of the smaller triangle

10+10=20 for area of the the 2 bigger triangles

4+4=8 for the area of the 2 smaller triangles

area of kite= 20+8= 28

By interpretating the graph of a quadratic equation, the initial height of the ball is equal to 5 feet above ground.

In this problem we must determine the initial height of the ball according to a graph, whose form resembles quadratic equations. Graphically speaking, the initial height is the y-coordinate of the y-intercept. First, the coordinates of the y-intercept of the equation are:

(t, h) = (0 s, 5 ft)

Second, the final height of the ball is equal to:

h = 5 ft

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Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

Answer:

right π/2

Step-by-step explanation:

The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .

Therefore, the correct answer is right π/2

Answer:

histogram

Step-by-step explanation:

The equation of the line that passes through the points (-2,4) and (-4,3) is y = (1/2)x + 5.

We know the slope intercept form of a line is given by:-

y = mx + c

Where,

m represents the slope of the line,

c represents the y-intercept, and

(x,y) represents the ordered pair of each point on the line

We know that,

m = (3-4)/(-4-(-2)) = -1/-2 = 1/2

We can write,

4 = (1/2)(-2) + c

4 = -1 + c

4 + 1 = c

c = 5

Hence, the equation of the line is :-

y = (1/2)x + 5

The graph of the equation is attached below.

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Answer:

the answer is 84 degrees

Step-by-step explanation: add 15 degrees to 69 degrees

Answer:

24.5025

Step-by-step explanation:

4.95 x 4.95=24.5025

Hope I helped!

Answer:

20 km

Step-by-step explanation:

if 15 percent is equal 3

then 5 percent is equal 1

if 15 * 6 = 90

and 10 percent equal 2

then 90 percent + 10 percent = 100 percent

6*3=18

18+2=20

so she needs to run 20 km for her long distance race .

Answer:

i think the radius is 9 because the diameter of the pool is 18 and the pool is in the shape of a circle so 9 is the best estimate.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

75-6=4y+4y+3.5y

or 11.5y=69

or y=69\11.5

     =6

Answer:

- 7.5 y - 4y= 6 - 75

Step-by-step explanation:

= - 11.5y = -69

= y = 6

As per the given inequality, the values according to it will be 8.001, 8.01, 8.1, 9, 11, 13, 16.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the information given in the question,

The given inequality is,

q > 8

The inequality show that the value of q must be greater than 8.

So, the values in increasing order is,

8.001, 8.01, 8.1, 9, 11, 13, 16.

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Answer:

Step-by-step explanation:

∠A = 90° because AC is diameter of the circle P.

Since ABC is right triangle and ∠A is 45°, the remaining angle is also 45°:

The function has three distinct real zeros.

The correct answer is A.

To determine the statement about the zeros of the graphed function, let's analyze the given information.

We have the following points on the graph:

(0.8, 4), (2, -4), (4.6, 0.5), (6, 0), and (7.5, 8)

Additionally, the function intercepts the x-axis at 1, 4, and 6 units.

To find the zeros of the function, we need to identify the x-values where the function intersects the x-axis.

From the given information, we know that the function intersects the x-axis at 1, 4, and 6 units.

These three x-values correspond to three distinct real zeros of the function.

The correct statement about the zeros of the graphed function is:

The function has three distinct real zeros.

The correct answer is A.

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(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

Let A represent the number of students reading Accountancy, S represent the number of students reading Sociology, and F represent the number of students reading French.

Let X be the number of students reading all three.

From the information given:

A ∩ S = 19

A + S - 27 = 120 - 53 + 19 = 86 (number of students reading Accountancy or Sociology but not French)

S - A - X = 27

S + F - X = 53

F - X = 19

A - X = 86 - 19 = 67

Total = A + S + F - (A ∩ S) - (A ∩ F) - (S ∩ F) + X = 120

Solving, we get X = 6, A = 73, S = 52, F = 25.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

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