Which equation has real zeros corresponding to
the x-intercepts of the graph?
y = log3(x) – 1
y = 3x - 3
y=-3(x - 1) + 3
y = log3(2x) - 2

Answer

a) Linear because there is a constant slope

b) Linear: y=x

Non-linear: y=1/x

Step-by-step explanation:

First we find the slope using the formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

For the points (0,2) and (1,3), we have

[tex]m = \frac{4-3}{1-0} = \frac{1}{1} = 1[/tex]

For the points (0,2) and (2,4), we have

[tex]m = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1[/tex]

For (1,3) (2,4), we have;

[tex]m = \frac{4 - 3}{2 - 1} = 1[/tex]

Since there is a constant rate of change the graph represents a linear function.

b) For a linear function, the highest degree is 1.

An example of a linear function is y=2x

For a non-linear function the degree of the variable is not equal to 1.

[tex]y = \frac{1}{x} [/tex]

The choices are missing, but we can solve the problem from the given information

Answer:

The equation which represents the circle is (x - 2)² + (y + 1)² = 16

Step-by-step explanation:

The form of the equation of a circle is (x - h)² + (y - k)² = r², where

∵ The coordinates of the center of the circle are (2 , -1)

∴ h = 2 and k = -1

The radius of the circle is the segment whose join the center of the circle and any point on the edge of the circle

∵ The circle passes through point (-2 , -1)

∴ The radius of the circle is the distance from the center (2 , -1)

    and the point (-2 , -1)

The y-coordinates of the two points are equal that means the radius is a horizontal segment and its length is the difference between their x-coordinates

∵ r = 2 - (-2)

∴ r = 4

Now let us substitute h, k, and r in the form of the equation of the circle

∵ (x - 2)² + (y - -1)² = (4)²

∴ (x - 2)² + (y + 1)² = 16

The equation which represents the circle is  (x - 2)² + (y + 1)² = 16

Henry has 13 chances to get a second turn.

Step-by-step explanation:

When two number cubes numbered from 1 to 6 are rolled, the number of possible outcomes are 36.

The 36 possible outcomes are as follows :

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6).

It is given that, Henry gets the second turn if he rolls a sum that is an even number less than 10.

Therefore, the even numbers less than 10 are {2,4,6,8}.

Check for the sum of outcomes that gives the result of even number less than 10.

The total number of chances to get second turn = 3+3+2+2+2+1 = 13 chances.

Therefore, Henry has 13 chances to get a second turn.

The numerical limits for a D grade in psychology can be calculated using the Z-score formula. The cutoff scores are below the top 84% and above the bottom 8%. Using the mean of 65.4 and the standard deviation of 9.7, the numerical limits for a D grade are 52 to 79.

To find the numerical limits for a D grade, we need to determine the cutoff scores. According to the given scheme, a D grade corresponds to scores below the top 84% and above the bottom 8%. To calculate these cutoff scores, we can use the Z-score formula. The Z-score is calculated as the difference between a score and the mean, divided by the standard deviation. Using the Z-score table, we can find the Z-scores corresponding to the top 8% and the bottom 8%. Finally, we can use the Z-score formula to find the corresponding scores for those Z-scores.

Given that the mean is 65.4 and the standard deviation is 9.7, we can calculate the Z-scores:

Z-score for the top 8% = 1.405

Z-score for the bottom 8% = -1.405

Using the Z-score formula, where X is the score, the mean is 65.4, and the standard deviation is 9.7:

X = Z * standard deviation + mean

For the top 8%:

X = 1.405 * 9.7 + 65.4 = 79

For the bottom 8%:

X = -1.405 * 9.7 + 65.4 = 52

Therefore, the numerical limits for a D grade are 52 to 79 (rounded to the nearest whole number).

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Answer:

1/5

Step-by-step explanation:

y2 -y1/x2 - x1

5 - 6/ -2 - 3

-1/-5

1/5

Answer:

2500

Step-by-step explanation:

Answer: 50x50 is 2500

Step-by-step explanation:

5x5=25

you have two 0s you never used add them to the end of the answer giving you not 25 but 2500

The triangle STV is not a right angled triangle.

Explanation:

Given that STV is a triangle with side lengths of 7, 11 and 14 units

We need to determine that STV is a right angled triangle.

Using Pythagorean theorem, we have,

[tex]c^2=a^2+b^2[/tex]

where [tex]c=14, a=7[/tex] and [tex]b=11[/tex]

Substituting the values in the above formula, we have,

[tex]14^2=7^2+11^2[/tex]

Squaring the terms, we get,

[tex]196=49+121[/tex]

[tex]196=170[/tex]

Since, both sides of the equation are not equal, then the triangle STV is not a right angled triangle.

Final answer:

To determine if triangle STV is a right triangle, apply the Pythagorean theorem. The theorem shows that STV is not a right triangle because the squares of the two shorter sides do not add up to the square of the longest side.

Explanation:

To determine whether triangle STV with side lengths of 7, 11, and 14 units is a right triangle, we can use the Pythagorean theorem. Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, if c represents the length of the hypotenuse and a and b represent the lengths of the other two sides, then the triangle is right if and only if c² = a² + b².

For triangle STV, let's assign the longest side, which is 14 units, as the hypotenuse c, and the other two sides as a and b. So:

a = 7 units

b = 11 units

c = 14 units

Now, we check:

c² = 14² = 196
a² + b² = 7² + 11² = 49 + 121 = 170

Since 196 does not equal 170, we conclude that triangle STV is not a right triangle.

The flag is 31.6 feet from the bottom of the sailboat.

Step-by-step explanation:

Step 1:

In the given triangle, the angle is 58°. Assume the opposite side has a length of x feet and the adjacent side has a length of 16 feet.

To determine the length of the opposite side of the triangle, we use the tan of the given angle.

[tex]tan \theta = \frac{oppositeside}{adjacent side} .[/tex]

Step 2:

In the given triangle,

The length of the opposite side = x feet,

The length of the adjacent side = 16 feet,

The angle of the triangle = 58°.

[tex]tan \theta = \frac{oppositeside}{adjacent side} , tan 58 = \frac{x}{16}, tan 58 = 1.6000.[/tex]

[tex]1.6 = \frac{x}{16} , x = (1.6)(16) = 25.6.[/tex]

Since Shianne's eyes are 6 feet from the bottom of the sailboat, the distance between the flag and the bottom of the sailboat [tex]= 25.6 + 6 = 31.6.[/tex]

So the flag is 31.6 feet from the bottom of the sailboat.

Answer:

[tex]19x+36[/tex]

Step-by-step explanation:

Answer:

The number is 12

Step-by-step explanation:

Step 1:  Convert words into an expression

Twelve less than a product of a number and 6 is 60

(n * 6) - 12 = 60

Step 2:  Solve for n

(n * 6) - 12 + 12 = 60 + 12

n * 6 / 6 = 72 / 6

n = 12

Answer:  The number is 12

8.039 has three decimal places which are the tenths, hundreths, and the thousandths.

Answer:

1/2

Step-by-step explanation:

The slope of Y = 1/2x + 1 is 1/2.

In a typical equation, there are 4 parts: Y, M, X, and B (since an equation in standard form is Y = MX + B. Y and X are typically variables, unless you fill them in with coordinate points to solve for B. B is the Y intercept, or where the line crosses the Y axis, and M is the slope of the line.

Thus meaning 1/2 is the slope for the equation given.

I hope this helps!

Step-by-step explanation:

[tex] \sin \: \phi = \cos( \phi + 20 \degree) \\ \\ \therefore \: \cos (90 \degree - \phi )= \cos( \phi + 20 \degree) \\ \\ \therefore \: 90 \degree - \phi = \phi + 20 \degree \\ \\ \therefore \: 90 \degree - 20 \degree = \phi +\phi \\ \\ \therefore \: 70 \degree = 2\phi \\ \\ \therefore \: \phi = \frac{70 \degree}{2} \\ \\ \huge \red { \boxed{ \therefore \: \phi = 35 \degree}}[/tex]

Answer:

36

Step-by-step explanation:

[tex]4 \times {t}^{2} = 4 \times {3}^{2} \\ = 4 \times 9 \\ = 36[/tex]

Answer:

42

Step-by-step explanation:

3 * (18 - 4) = 3 * 14 = 42

Answer:

42

Step-by-step explanation:

18-4=14. 14*3=42

Answer:

Option 3)

8(a + 7) can be rewritten as 8(a) + 8(7).

Option 7)

An equivalent expression is 8a + 56

Step-by-step explanation:

We are given the following expression:

[tex]8 (a + 7)[/tex]

We can simplify the expression by distributing 8 over (a+7).

Distributive property:

[tex]a(b+c)\\=(a\times b) + (a\times c)\\=a(b) + a(c)\\=ab + ac[/tex]

Simplifying the expression, we get,

[tex]8(a+7)\\=(8\times a)+(8\times 7)\\=8a + 56[/tex]

Thus, the correct options are:

Option 3)

8(a + 7) can be rewritten as 8(a) + 8(7).

Option 7)

An equivalent expression is 8a + 56

The true statements about the expression 8(a+7) are 2, 3 and 7.

When evaluating the expression 8(a+7), several steps can be taken to rewrite or simplify it. Here's a closer look at the provided statements:

Statement 1 suggests to distribute 'a' to 8 and to 7, which is incorrect. The correct procedure is to distribute the 8 to both 'a' and the 7.

Statement 2 correctly suggests that 8(a) can be rewritten as 8a.

Statement 3 is true, as 8(a+7) can be rewritten following the distributive property as 8(a)+8(7), which simplifies to 8a+56.

Statement 4 is incorrect because it omits the distribution of 8 over both terms within the parentheses.

Statement 5 is incorrect as there is no reason to believe that 8(a+7) simplifies to 15a without any additional information.

Statement 6 is incorrect as it implies that the 8 is only multiplied by 'a' and not by the 7.

Statement 7 is correct because the expression 8(a+7) is correctly expanded to 8a+56.

Answer:

Step-by-step explanation:

-2p-4=2

Collect like terms

-2p=2+4

-2p=6

p=6/-2=-3

Answer:

p=-3

Step-by-step explanation:

-2p-4=2

add 4 to both sides then get -2p =6

divide both sides by -2 and get p=-3

Hope this helped

Answer:

Angle A = 78

Step-by-step explanation:

Start with the equation 8x+20=180 and solve for x which equals x=20. You then substitute for x with the equation for angle A. A=3(20)+18 which makes angle A = 78

The measure of ∠A is 78 degrees.

Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles.

Which means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

∠A and ∠B are supplementary angles. If ∠A=(3x+18) and ∠B=(5x+2)

then find the measure of ∠A.

Now Start with the equation

8x+20 = 180

solve for x which equals x=20.

then substitute for x with the equation for angle A.

A=3(20)+18

angle A = 78

Hence, the measure of ∠A is 78 degrees.

Learn more about supplementary angles here:

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Answer:

27 = 3 , 3, 3

63= 3 , 3, 7

54= 3 , 3, 3, 2

HCF OF 27, 63 AND 54 = 3 X 3 = 9

HOPE THIS HELPS YOU MATE Plz mark it as brainliest answer

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Answer:

Commutative property:  The formula for this property is a + b = b + a. For example, adding 1 + 2 or 2 + 1 will give us the same answer according to the commutative property of addition.

Answer:

4 and 6

:)

EDGE 2020

Answer:

B) 4

C) 6

Step-by-step explanation:

Answer: The coordinates of point B are (19 , 20).

Step-by-step explanation:

The mid point (x,y) of line joining (a,b) and (c,d) is given by :-

[tex](x,y)=(\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex]                        (1)

Given : Point A is located at (3,6). The midpoint of line segment AB is point C(11,13).

Let the coordinates of point B are (a,b) m, the according to (1) , we have

[tex](\dfrac{3+a}{2},\dfrac{6+b}{2})=(11,13)\\\\\Rightarrow\ \dfrac{3+a}{2}=11\ \ ,\ \ \dfrac{6+b}{2}=13\\\\\Rightarrow\ 3+a=22\ \ ,\ \ \ 6+b=26\\\\\Rightarrow\ a=19,\ \ b= 20[/tex]

Hence, the coordinates of point B are (19 , 20).

16 gallons will be burned

Answer: The height of the pole is 26 ft

Step-by-step explanation: Please refer to the attached diagram for details.

The diagram shows a right angled triangle labeled PEG. The point P is the top of the flagpole, the point E is the eye level of the observer, while point G is the point where the flagpole touches the ground. However, we must not forget that the observer’s eye is 5 ft from the ground. This means the height of the flagpole in the triangle has an extra 5 ft that would be added after our calculation. So, we have an opposite, which is the unknown and an adjacent, which is the side that lies between the reference angle and the right angle (that is, 30). Also we have the reference angle as 35.

Using the trigonometric ratios,

TanE = opposite/adjacent

Tan35 = PG/30

By cross multiplication we now have

Tan35 x 30 = PG

0.7002 x30 = PG

21.006 = PG

The height of the pole is approximately 21 ft.

However, we remember that the eye of the observer is 5 ft away from the ground. That means the pole actually goes an additional 5ft when it touches the ground. Hence the actual length of the pole is 21 + 5 = 26

Height of pole = 26 ft

Answer:

-1

Step-by-step explanation:

Step 1:  Combine

(-3) + (-2) - (-4)

Two negatives - (-4) makes a positive +4

-3 - 2 + 4

-1

Answer:  -1

Answer:

-1

Step-by-step explanation:

It's quite simple! It is just like normal addition and subtraction but add the negative! Sorry it's a pretty bad response haha

-3-2+4

The expression which is equivalent to 2⁵ is, 2×2×2×2×2

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The given expression is  2⁵

Equivalent expression = ?

Given expression can be write in the factors of  2⁵

⇒ 2⁵ = 2×2×2×2×2

Hence, The equivalent expression is 2×2×2×2×2

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Answer:

  Replace "is" with an equal sign.

Step-by-step explanation:

It looks like you want the equation ...

  -9 = -16

which makes no sense at all. Perhaps you intend ...

  -g = -16

Area of building is [tex]3,84,000m^3[/tex] .

Step-by-step explanation:

Here we have , a figure in given below picture where we have to find volume of this office building , Let's find out:

If we look closely we see that it's basically cuboid with dimensions 50 m by 110 m by 70 m . But there's one small cuboid sliced off from this cuboid with dimensions 50 m by 10 m by (110-90) m i.e.  50 m by 10 m by 20 m .

Area of building = Area of larger cuboid - Area of smaller cuboid

Area of cuboid = [tex]length(width)(breadth)[/tex]

⇒ Area of building = Area of larger cuboid - Area of smaller cuboid

⇒ [tex]Area = (50(110)(70))m^3 - (50(10)(20))m^3[/tex]

⇒ [tex]Area = 3,85,000m^3 - 10,000m^3[/tex]

⇒ [tex]Area = 3,84,000m^3[/tex]

Therefore, Area of building is [tex]3,84,000m^3[/tex] .