The system of equations shown below is graphed on a coordinate grid:

3y + x = 4
2y − x = 6

Which statement is true about the coordinates of the point that is the solution to the system of equations?
It is (−2, 2) and lies on both lines.
It is (−5, 3) and lies on both lines.
It is (−5, 3) and does not lie on either line.
It is (−2, 2) and does not lie on either line.

Answer:

Step-by-step explanation:

Terms  

7

3d²

d⁴

Constant : 7

Coefficient of 3d²  = 3

Coefficient of d⁴ = 1

Final answer:

The expression 7 + 3d2 + d4 contains terms 7, 3d2, and d4, with coefficients 3 and 1 (implicit), and the constant 7. We identify each part according to algebraic principles and ensure to simplify and check our work.

Explanation:

The expression given is 7 + 3d2 + d4, which is a polynomial in d. The terms in this expression are 7, 3d2, and d4. Each part of a term can be classified as follows:

The coefficients are the numerical factors of the variables, which in this case are 3 for the term 3d2 and 1 for the term d4 (note: the coefficient is implicitly 1 here, since it's not written).

The constants are terms that do not contain variables, which here is only the number 7.

As a part of algebra, it's important to eliminate terms where possible to simplify the algebra and always check the answer to see if it is reasonable.

Answer:

yes

Step-by-step explanation:

A proportional relationship has the form

y = kx ← k is the constant of proportionality

y = 24x ← is in this form and is proportional with k = 24

Answer:

1,787.75

Step-by-step explanation:

The sum of the areas of the 10 rectangles gives the surface area of the cushion:

A  = 140 sq. in. + 80 sq. in. + 121 sq. in. + 2(605 sq. in.) + 22 sq. in. + 2(68.875) sq. in +19 sq. in. + 58 sq. in.

= 140 sq. in. + 80 sq. in. + 121 sq. in. + 1,210 sq. in. + 22 sq. in. + 137.75 sq. in +19 sq. in. + 58 sq. in.

= 1,787.75 sq. in.

The surface area of the cushion is 1,787.75 square inches.

Answer:

87.28 cubic inches

Step-by-step explanation:

Leigh wants to fill the conical candle wax mold completely with candle wax.

We have to calculate the volume of the cone by the formula :

[tex]V=\pi r^2\frac{h}{3}[/tex]

Here, V = volume

r = radius = 2.1 inches

h = height = 18.9 inches

By substituting these values given, into the formula

[tex]V=\pi (2.1)^2(\frac{18.9}{3})[/tex]

   = (27.783)π

   = 87.28 inch³

Conical mold can hold 87.28 inch³ candle wax.

Words typed in 1 minute = 70

Words typed in 12 minutes = 70 x 12 = 840 words

If Miko types at 70 words per minute, in 12 minutes he can type 840 words if he maintains the same speed throughout.

Answer:

f(2) = 7

Step-by-step explanation:

To figure this out you just have to plug in 2 wherever x is in the equation.

f(2) = 5(2) - 3

Multiply 5 by 2

f(2) = 10 - 3

Subtract

f(2) = 7

5 is correct

5/6 = 15/18

Answer:

=6/7x^3

Step-by-step explanation:

36x^4/42x^7

(36/42)(x^4/x^7)

6/7(x^-3)

6(x^-3)/7

6/7x^3

Answer:

If it is horizontal then it is zero, if it is vertical then it is undefined

Step-by-step explanation:

horizontal=  <------------->

             ^

vertical=|    (up and down)

             v

Answer:

undefined

Step-by-step explanation:

Answer:

the answer is C: 90

Step-by-step explanation:

if its across from the number then its gonna be the same

Answer:

c: 90°

Step-by-step explanation: The lines are a reflection of each other, so the 90° angle is the same as B. :) sorry if my explanation is bad.

Answer:

sin(74º) = 0.96

Step-by-step explanation:

answer is 70

When rounding to the nearest tenth like 74 we:

Round the number to the nearest tenth if the last digit of the number is 5678 or 9

Then we do the same rounding it down

Answer:c

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

f(x) = 6x-4

Let x=8

f(8) = 6*8 -4

    = 48 -4

    =44

Answer:

44

Step-by-step explanation:

f(x) = 6x – 4

f(8) = 6(8) – 4

= 48 - 4

= 44

Answer:

The total amount of fishes  caught is 414,519 fishes

Step-by-step explanation:

Here, given the percentage decrease in the population of fishes, we want to know the total amount of fishes caught by the company in the first 7 years.

First year, we have 75,000 fishes

Second year, we would have 75,000 - (8% of 75,000) = 75,000 - (0.08 × 75,000) = 75,000 - 6,000 = 69,000

Third year, we would have 69,000- (0.08 × 69,000) = 69,000 - 5520 = 63,480

Fourth year, we would have 63,480 - (0.08 × 63,480) = 58,401.6

Fifth year, we would have 58,401.6 - (0.08 × 58,401.6) = 58,401.6 - 4,672.18 = 53,729.472

Sixth year, we would have 53,729.472 - (0.08 × 53,729.472) = 53,729.472 - 4,298.3578 = 49,431.114

Seventh year, we would 49,431.114 - (0.08 × 49,431.114) = 45,476.625

The addition of all these values will give the total number of fishes caught = 75,000 + 69,000 + 63,480 + 58,401.6 + 53,729.472 + 49,431.114 + 45,476.625 = 414,518.8 = 414,519 fishes to the nearest whole number

Final answer:

Learn how to calculate the total fish caught by a fishing company over 7 years with decreasing catches.

Explanation:

A major fishing company caught 75,000 fish in the first year. Each year, the number of fish caught decreased by 8%. To find the total fish caught over 7 years:

Calculate the number of fish caught each year by multiplying the previous year's catch by (100% - 8%).

Add up the catches for 7 years.

Round the final total to the nearest whole number.

Therefore, the fishing company caught approximately X fish over the first 7 years.

Answer:

4 x 10^12

Step-by-step explanation:

I used a calculator.

(6x10^8) divided by (1.5 x 10^-4) is 4 x 10^12.

Division is the action of separating something into parts or the process of being separated.

How to solve?

While dividing;

[tex]\frac{6(10^8)}{1.5(10^-4)} \\\frac{6(10^8)(10^4)}{1.5}\\ 4(10^{12})[/tex]

The answer will be 4 x 10^12.

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Answer: Kelsey graphed the slope as the y-intercept and the y- intercept as the slope.

Step-by-step explanation:

Answer: D on edg

Step-by-step explanation:

Kelsey graphed the slope as the y-intercept and the y- intercept as the slope.

Answer:

B

Step-by-step explanation:

Answer:

A. 5.3%

Step-by-step explanation:

Answer:

I assume the answer would be that f(x) = 6(x) increases over the interval x = 3 to x = 4

Step-by-step explanation:

6 x 3 is 18 and 6 x 4 is 24, so over the interval x = 3 to x = 4 f(x) would increase.

Answer:

16

Step-by-step explanation:

The radius is half the size of the diameter.

8 * 2 = 16

Answer:

It can be factorised

Step-by-step explanation:

Given

x²y² + 36 - 4x² - 9y² ( rearranging )

x²y² - 4x² - 9y² + 36 ( factor first/second and third/fourth terms )

= x²(y² - 4) - 9(y² - 4) ← factor out (y² - 4) from each term

= (y² - 4)(x² - 9)

Both factors are a difference of squares and factor in general as

a² - b² = (a - b)(a + b)

Thus

y² - 4

= y² - 2² = (y - 2)(y + 2) , and

x² - 9

= x² - 3² = (x - 3)(x + 3)

Hence

x²y² + 36 - 4x² - 9y² = (y - 2)(y + 2)(x - 3)(x + 3)

Answer:

[tex] area = 21.11 ~in.^2 [/tex]

Step-by-step explanation:

Area of sector of circle with central angle measuring n degrees and radius r:

[tex] area = \dfrac{n}{360^\circ}\pi r^2 [/tex]

[tex] area = \dfrac{80^\circ}{360^\circ} \times 3.14 \times (5.5~in)^2 [/tex]

[tex] area = \dfrac{80^\circ}{360^\circ} \times 3.14 \times (5.5~in)^2 [/tex]

[tex] area = 21.11 ~in.^2 [/tex]

The area of the sector of the circle will be 21.12 inch².

The area of sector of circle central angle θ in degree and radius r will be represented as

A= (θ/360°)πr²

the sector has a central angle θ=80°

r=5.5 inches

substituting these values in above formula for the area of the sector of circle,

Area= A

= (θ/360°)πr²

= (80°/360°)π(5.5)²

=21.12 inch²

Therefore, the area of the sector will be 21.12 inch².

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Answer:

Length = 4 units

Step-by-step explanation:

Width = x units

Length = (x + 4) units

Area = 32 square units

length * width = 32

(x +4) *x = 32

x *x + 4 * x = 32

x² + 4x  -32 = 0

Sum = 4

Product = -32

Factor = 8 , (-4)

x² + 4x  -32 = 0

x² + 8x - 4x - 4 * 8 = 0

x(x + 8) - 4(x +8) = 0

(x + 8) (x - 4) = 0

(x + 8) is ignored because measurements will not have negative sign.

x-4 =0

x = 4

Width = 4 units

Length = x + 4 = 4 + 4 = 8 units

Answer:

no solution

Step-by-step explanation:

–5x – 12y – 43z = –136

–4x – 14y – 52z = –146

21x + 72y + 267z = 756

Every coefficient of the second equation is a multiple of 2, so divide both sides by 2.

Every coefficient of the third equation is a multiple of 3, so divide both sides by 3.

–5x – 12y – 43z = –136

–2x – 7y – 26z = –73

 7x + 24y + 89z = 252

Let's call the above system the "simplified original system."

Using the simplified original system, multiply the first equation by -2 and the second equation by 5. Then add them.

         10x + 24y + 86z = 272

(+)      -10x - 35x - 130z = 365

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

                  -11y - 44z = 637

Now we have an equation with only y and z.

Now, using the simplified original system, multiply the second equation by 7 and the third equation by 2. Then add them.

       –14x – 49y – 182z = –511

(+)       14x + 48y + 178z = 504

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

                    -y - 4z = -7

Now we have a system in 2 unknowns, y and z.

-11y - 44z = 637

-y - 4z = -7

Multiply the second equation by -11 and add to the first equation.

     -11y - 44z = 637

(+)     11y + 44z = 77

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

                0 = 714

Since 0 = 714 is false, this system has no solution.

Answer:

D: Lauren made her first error in step 3 because she should have used 85-60 = 25 for chemistry and 80-60 = 20 for biology

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Got it right on ed 2020

Answer:

Always true

All real numbers

Step-by-step explanation:

The given equation 1/6(12z-18)=2z-3 has no solution.

The given equation is 1/6(12z-18)=2z-3.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, 1/6(12z-18)=2z-3

12z/6 -18/6 =2z-3

2z-3=2z-3

Transpose 3 to other side of the equation, we get

2z=2z-3+3

2z = 2z

Transpose 2z to other side of the equation, we get

2z-2z=0

Therefore, the given equation has no solution.

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Answer:

(a) C: 0.0465 ; reject the null hypothesis

(b) B: 0.3409 ; fail to reject the null hypothesis

Step-by-step explanation:

Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;

(a) Now, we are given alternate hypothesis, [tex]H_1[/tex] : p < 3/5

Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;

             P-value = P(Z < -1.68) = 1 - P(Z [tex]\leq[/tex] 1.68)

                           = 1 - 0.95352 = 0.0465

Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which we reject the null hypothesis.

(b) Now, we are given alternate hypothesis, [tex]H_1[/tex] : p > 0.383

Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;

             P-value = P(Z > 0.41) = 1 - P(Z [tex]\leq[/tex] 0.41)

                           = 1 - 0.6591 = 0.3409

Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which we fail to reject the null hypothesis.

To determine the null hypothesis's fate, compare the p-value to α = 0.05. For the first scenario, H1: p < 3/5 with the test statistic z = -1.68, the conclusion is unclear without the exact p-value. For the second scenario, H1: p > 0.383 with z = 0.41, we fail to reject the null hypothesis as the p-value (0.3409) is higher than α.

The task is to compare the p-value to the significance level (alpha, α) to determine if the null hypothesis should be rejected or not. If the p-value is less than or equal to α, reject the null hypothesis; otherwise, fail to reject it. The significance level given is α0.05.

First Scenario:

For H1: p < 3/5, the test statistic z = -1.68. Comparing the test statistic to the critical value for α=0.05 (which is between -1.65 and -1.64), -1.68 falls to the left of -1.65. However, without the exact p-value provided, the answer cannot be definitively chosen from the options. Still, the general rule is that if the test statistic is more extreme than the critical value, the null hypothesis is rejected.

Second Scenario:

For H1: p > 0.383, the test statistic z = 0.41. The p-value corresponding to z = 0.41 on the upper tail of a standard normal distribution is approximately 0.3409 (since the p-value is the area to the right of z). Therefore, the p-value is greater than α0.05, meaning that we fail to reject the null hypothesis.

Answer:

16,048 visitors per day.

Step-by-step explanation:

To solve for this answer, you will simply need to divide the total amount of visitors (48,144) by the amount of days given, which in this instance, is 3.

48,144÷3= 16,048 visitors per day.