Expand & simplify (x - 1)(x + 5) ​

Answer:

for y=x-1 y=-1 and for y=x2 y=0

Step-by-step explanation:

to find the y intercept substitute x=0 so you have your answer y=-1 and y=0  

Answer:

x+2

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Answer:

Step-by-step explanation:

x-1, because 3 fits the criteria, x>=1

The answer is:

\(\large\textbf{They aren't equivalent.}}\)

In-depth explanation:

To determine the answer to this problem, we will use one of the exponent properties:

\(\sf{x^{-m}=\dfrac{1}{x^m}}\)

And

\(\sf{\dfrac{1}{x^{-m}}=x^m}\)

Now we apply this to the problem.

What is 4⁻³ equal to? Well according to the property, it's equal to:

\(\sf{4^{-3}=\dfrac{1}{4^3}}\)

And this question asks us if 4⁻³ is the same as 1/4⁻3.

Well according to the calculations performed above, they're not equivalent.

Answer:

11/2y

Step-by-step explanation:

Let's solve for x.

y=2x−10y

Step 1: Flip the equation.

2x−10y=y

Step 2: Add 10y to both sides.

2x−10y+10y=y+10y

2x=11y

Step 3: Divide both sides by 2.

2x

2

=

11y

2

x=

11

2

y

Answer:

11/2y.....................

If you are filling traffic cones with sand to keep them from blowing over and the cone has a radius of 7 inches and a height of 28 inches, then 1436 cubic inches of sand can fit inside the cone.

The volume of the cone can be described as the measure of a 3-D space occupied by matter.

The volume of sand in cubic inches that can fit inside the traffic cone can be calculated by the formula,

v = πr²h / 3

As the radius of the cone = 7 inches

Height of the cone = 28 inches

v = π(7)²28 / 3

v = (π)(49)(28) / 3

v = (π)(1372) / 3

As π = 3.14

v = (3.14)(1372) / 3

v = 4308.08 / 3

v = 1436.02 ≈ 1436 cubic inches

Hence, 1436 cubic inches of sand is calculated to fit inside the cone.

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Answer:

The mode of the data set is 83.

Step-by-step explanation:

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

50   51   53   55   58   59   63   65   66   66   67   71   72   72   77   79   80   83   83   83   84   86   88   88   92   94   94   97   97   99  

We see that the mode is 83 .

Option a) $213.34 is the correct answer.

Given that, Suppose that you are 34 years old now and that you would like to retire at the age of 75. Furthermore, you would like to have a retirement fund from which you can draw an income of $70,000 annually. You plan to reach this goal by making monthly deposits into an investment plan until you retire. The amount to be deposited each month needs to be calculated. It is assumed that the annual interest rate is 8% and compounded monthly.

The formula for the future value of the annuity is given by, \(FV = C * ((1+i)n -\frac{1}{i} )\)

Where, FV = Future value of annuity

            C = Regular deposit

            n = Number of time periods

            i = Interest rate per time period

In this case, n = (75 – 34) × 12 = 492 time periods and i = 8%/12 = 0.0067 per month.

As FV is unknown, we solve the equation for C.

C = FV * (i / ( (1 + i)n – 1) ) / (1 + i)

To get the value of FV, we use the formula,FV = A × ( (1 + i)n – 1 ) /i

where, A = Annual income after retirement

After substituting the values, we get the amount to be deposited as $213.34.

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The probability of getting 2 or more heads in 5 successive coin tosses is 13/16 or approximately 0.8125.

To calculate the probability of getting 2 or more heads in 5 successive tosses of a fair coin, we need to consider all the possible outcomes that satisfy this condition.

The total number of possible outcomes when tossing a coin 5 times is 2^5 = 32, as each toss has 2 possible outcomes (heads or tails).

To find the probability of getting 2 or more heads, we need to calculate the probability of the complementary event, which is getting 0 or 1 head and subtract it from 1.

The probability of getting 0 heads (all tails) is (1/2)^5 = 1/32.

The probability of getting 1 head and 4 tails is (5 choose 1) * (1/2)^5 = 5/32.

Therefore, the probability of getting 2 or more heads is 1 - (1/32 + 5/32) = 26/32 = 13/16.

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Answer:

Step-by-step explanation:

1).

Answer:

12

Step-by-step explanation:

144/16=9

Each child gets sixteen coins if there are nine children.

9+3=12

There are three more children so there are twelve.

The measures can be classified as follows:

a) qualitative, b) qualitative,  c) quantitative, d) quantitative, and

e) qualitative.

a) The genders of the first 40 newborns in a hospital one year can be categorized as qualitative data. Gender is a categorical variable that can be classified as either male or female.

b) The natural hair color of 20 randomly selected fashion models is also qualitative data. Hair color is a categorical variable that can have various categories like blonde, brunette, red, etc.

c) The ages of 20 randomly selected fashion models can be classified as quantitative data. Age is a numerical variable that can be measured and expressed in numbers.

d) The fuel economy in miles per gallon of 20 new cars purchased last month is a quantitative measure. It represents a numerical value that can be measured and compared.

e) The political affiliation of 500 randomly selected voters is qualitative data. Political affiliation is a categorical variable that represents different affiliations such as Democrat, Republican, Independent, etc.

In summary, measures (a) and (b) are qualitative, measures (c) and (d) are quantitative, and measure (e) is qualitative.

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Answer:

  -7/10

Step-by-step explanation:

You want the value of |a +3|÷(a -3) when a = -17.

Put the value where the variable is and do the arithmetic.

  |-17 +3| ÷ (-17 -3)

  = |-14| ÷ (-20) . . . . . . . . . . simplify

  = 14/(-20) = -14/20 . . . . . absolute value

  = -7/10 . . . . . . . . . . . . reduce the fraction

The value of the expression is -7/10.

__

Additional comment

A calculator or spreadsheet can help.

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Answer:

31°,59°

Step-by-step explanation:

csc (2x+9)=sec(3x+26)

1/sin(2x+9)=1/cos (3x+26)

sin (2x+9)=cos(3x+26)

cos (90-2x-9)=cos(3x+26)

90=3x+26+2x+9

5x+35=90

5x=90-35=55

x=55/5=11

2x+9=2×11+9=31°

3x+26=3×11+26=59°

The correct answer is (D) The full length to which it can be extended.

The size classification of an extension ladder indicates the full length to which it can be extended.
An extension ladder's size classification indicates the total length the ladder can reach when its fly section is fully extended.

This helps users determine if the ladder will be long enough for their specific needs when working at height.

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Answer:

30.4

Step-by-step explanation:

80x38/100

Answer:

13 + \(\sqrt{89}\)

or

22.43398... (depends on how you round it)

Step-by-step explanation:

1. The question stated that the radius of the circle O is 5, so the length of AO and CO is 5.

2. Since line AB and line CB are both tangent to the circle, they have the same length. CB is 8, so AB will also be 8.

--> Both triangle AOB and COB share one side, and the other side (radius) has the same length, so the third side must be the same length

3. Tangent means having a 90-degree angle with the radius. We know that the triangle AOB is a right triangle since the angle OAB is 90 degrees.

We can use the Pythagorean theorem to find side OB. OB^2 = AO^2 + AB^2.

--> OB^2 = 25 + 64

--> OB^2 = 89

--> OB = \(\sqrt{89}\)

Now that we know the lengths of all three sides, we can add them up.

--> 5 + 8 + \(\sqrt{89}\)

--> 13 + \(\sqrt{89}\)

or

--> 22.43398113....

Answer:

2r+10-4r+4=32

-2r+14=32

-2r= 32-14

-2r=18

R= -9

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

a. CD = \(\sqrt{13}\), EF = \(\sqrt{13}\), CD≅EF

If \((x_{1}, y_{1})\) & \((x_{2}, y_{2})\) are co-ordinates of two points then the distance between this two points = \(\sqrt{(x_{2}- x_{1}) ^{2}+ (y_{2}- y_{1} )^{2} }\)

Here, Point C = (0, 4) & Point D = (3, 2)

Then CD = \(\sqrt{(3-0)^{2} +(2-4)^{2} }\) = \(\sqrt{3^{2} +(-2)^{2} }\) = \(\sqrt{9+4}\) = \(\sqrt{13}\)

And Point E = (-2, 1) & Point F = (-4, -2)

Then EF = \(\sqrt{((-4)-(-2))^{2}+ ((-2)-1)^{2} }\)= \(\sqrt{(-2)^{2} +(-3)^{2} }\)= \(\sqrt{4+9}\)= \(\sqrt{13}\)

We know that, if two line segment have same length, they are congruent.

Here CD = EF = \(\sqrt{13}\)

Since CD & EF have same length, so CD is congruent to EF.

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Therefore, the measure of the central angle whose radii define the given arc is approximately 83.077 degrees.

The length of an arc on a circle is given by the formula:

Arc Length = (Central Angle / 360°) * Circumference

In this case, we know the arc length is 6π centimeters, and the radius of the circle is 13 centimeters. The circumference of the circle can be calculated using the formula:

Circumference = 2π * Radius

Substituting the radius value, we get:

Circumference = 2π * 13

= 26π

Now we can use the arc length formula to find the central angle:

6π = (Central Angle / 360°) * 26π

Dividing both sides of the equation by 26π:

6π / 26π = Central Angle / 360°

Simplifying:

6 / 26 = Central Angle / 360°

Cross-multiplying:

360° * 6 = 26 * Central Angle

2160° = 26 * Central Angle

Dividing both sides by 26:

2160° / 26 = Central Angle

Approximately:

Central Angle ≈ 83.077°

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Answer:

N-16=(other persons time.)

Three measures of dispersion are range, variance, and standard deviation.

1. Range: The range is the difference between the highest and lowest values in a data set. To calculate the range, subtract the lowest value from the highest value.

2. Variance: Variance measures how spread out the values in a data set are. To calculate the variance, subtract the mean from each data point, square the result, sum up the squared differences, and divide by the total number of data points.

3. Standard deviation: Standard deviation is another measure of how spread out the values in a data set are. It is the square root of the variance. To calculate the standard deviation, calculate the variance first and then take the square root.

A fair coin tossed three times can have either a head (H) or a tail (T) outcome. To construct a tree diagram for this experiment, start with a root node representing the first toss. Then, create two branches for each toss, one representing a head outcome and the other representing a tail outcome. Repeat this process for the second and third tosses. The resulting tree diagram will have a total of 8 possible outcomes in the sample space: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT.

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Answer: 17600

Step-by-step explanation: 16000*10% is the same as 16000*0.1, then you get 1600. 16000+ 1600 is 17600

Answer:

Hello,

answer : 259269764699508231

Step-by-step explanation:

We must use permutations with repetitions

Formular for total surface area of a cylinder

S = 1231.5 sq ft

Answer:

B

Step-by-step explanation:

I learned this a while ago, if you have the < symbol then you shade below the dotted line. You can get the rest.

Answer:

x=10

Step-by-step explanation:

since the angles seem similar they're most likely to be the same but since its 3x and you have to find the value of x then we will do 3 x ?=30, which is 10. if you want to check there is one way, since the angle on a straight line is 180 you can do 180 - 30 =150 which will be the unknown value next to the given angle. Since the unknown angle is on the line with the 150 degree angle we can do 180 - 50 to get the unknown angle (3x) which is 30. So in conclusion x will be 10

Answer: x = 10

Step-by-step explanation:

The angles are voa which means vertically opposite angles which means they are conguerent and also equal

ATQ

⇒3x = 30

⇒x = 30/3

⇒x = 10

Therefore x = 10 degrees

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Answer:

6 1/10

Step-by-step explanation:

Answer

6 1/10

Step-by-step explanation:

2 3/5+3 1/2

2+3=5

3/5=6/10 find the common denominator  1/2=5/10

6/10+5/10=11/10

11/10=1 1/10

5+1 1/10= 6 1/10

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Based on the information given, if there's a VAT of 15%, the price of the shoe will be R902.75.

A value-added tax simply means the tax that's levied on a product. In this case, you didn't give the VAT percentage. Therefore, let's assume that the percentage is 15%.

In a situation whereby the pair of shoes are R785, the price of the shoe will be:

= 785 + (15% × 785)

= 785 + (0.15 × 785)

= 785 + 117.75

= R902.75.

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Answer:

Step-by-step explanation:

(1/2)(x+3)(2x+4)

= x^2 + 5x + 6

a=1

b=2

c=5

d=1

e=6