Solve each triangle. Round answers to the nearest tenth.

Observe that

[tex]x^2 + 3x + 1 = (x^2 + 4x + 4) - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - x - 3 \\\\ ~~~~~~~~ = (x + 2)^2 - (x + 2) - 1[/tex]

so that

[tex]P(x+2) = (x+2)^2 - (x+2) - 1 \implies P(x) = x^2 - x - 1[/tex]

Then

[tex]P(x - 1) = (x-1)^2 - (x-1) - 1 \\\\ ~~~~~~~~ = (x^2 - 2x + 1) - (x - 1) - 1 \\\\ ~~~~~~~~ = \boxed{x^2 - 3x + 1}[/tex]

Alternatively, we can avoid find [tex]P(x)[/tex] altogether and instead first write [tex]x-1[/tex] in terms of [tex]x+2[/tex] :

[tex]x - 1 = (x - 1) + 2 - 2 = (x + 2) - 1 - 2 = (x + 2) - 3[/tex]

Then

[tex]P(x - 1) = P((x + 2) - 3) \\\\ ~~~~~~~~ = (x - 3)^2 + 3 (x - 3) + 1 \\\\ ~~~~~~~~ = x^2 - 3x + 1[/tex]

Answer:

28 legs are on the ground

Answer:

Arithmetic sequence

Step-by-step explanation:

The given sequence is arithmetic because it is increases gradually by 5

so the answer is "an arithmetic" and "difference" is equal to "5"

The equation of the inverse function is given as n(t) = (t+3)/4

Given the function that is represented as;

[tex]t(n)=8\cdot\frac{n+3}{2}[/tex]

This is further simplified to have:

t(n) = 4(n + 3)

Replace t with t(n)

t = 4n - 3

Make n the subject of the formula

4n = t+3

n = (t+3)/4

Hence the equation of the inverse function is given as n(t) = (t+3)/4

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The interest that Marcos will get is 50000.

The following can be deduced from the information given:

Principal = 50000

Interest rate = 12.5%

Time = 8 years

The simple interest will be:

= (PRT/100)

= (50000 × 12.5 × 8)/100

= 50000

The amount that will be obtained after 8 years will be:

= Principal + Interest

= 50000 + 50000

= 10000

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Answer:

The interest that Marcos will get is 50000.

Based on the calculations, the area of this triangle is equal to: A. Area = 1/2 × [√(x₂² + y₂²) × √(x₁² + x₁²)].

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

Next, we would find the distance between points A and B:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

AB = √[(x₂ - 0)² + (y₂ - 0)²]

AB = √(x₂² + y₂²)

Also, we would find the distance between points A and C:

Distance = √[(x₁ - x₂)² + (y₁ - y₂)²]

AC = √[(x₁ - 0)² + (y₁ - y0)²]

AC = √(x₁² + x₁²).

Now, we can find the area of this triangle:

Area = 1/2 × b × h

Area = 1/2 × AB × AC

Area = 1/2 × [√(x₂² + y₂²) × √(x₁² + x₁²)]

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Answer: B. 1/2√(x2^2 - x1^2) ( y2^2 - y1^2

Step-by-step explanation: Edmentum

The measure of side c if a is 5 cm and b is 9 cm in a right triangle is √106 cms.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

The measure of side c if a is 5 cm and b is 9 cm in a right triangle will be,

c² = 5² + 9²

c = √106 cms

Hence, the measure of side c if a is 5 cm and b is 9 cm in a right triangle is √106 cms.

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Answer:

x=180 - 25

x=155

x+ 169=180

x=180-169

x=11

The true statement that explains the correlation coefficient is: C. As the baby gains weight, the prices of smartphone tend to increase.

The value of the correlation coefficient shows a relationship between two variables. A positive value suggests a positive relationship, meaning as one variable increases, the other also increases.

A correlation coefficient of  0.87 suggests a positive relationship between baby's weight and the price of smartphone, therefore, the true statement is:

C. As the baby gains weight, the prices of smartphone tend to increase.

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Answer:

8

Step-by-step explanation:

The equation of the parabola can be represented as

[tex]y = a(x + 1)(x - 5)[/tex]

for some constant a.

Since the coefficient of x² is 2, a = 2, so

[tex]y = 2(x + 1)(x - 5) \\ \\ y = 2( {x}^{2} - 4x + 5) \\ \\ y = 2 {x}^{2} - 8x + 10[/tex]

So, the answer is 8.

Answer:

C

Step-by-step explanation:

you can only work 40 or less hours per week but you must earn greater then or equal to $323.

The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.

Answer:

The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.

Step-by-step explanation:

Answer:

-28

Step-by-step explanation:

x/4= -7

4* x/4= -7*4

x= -28

The value of x in the straight line shown in the attached diagram is 64°

An equation is an expression that shows the relationship between two or more variables and numbers.

From the image:

x + 26 + 90 = 180° (sum of angles in a straight line)

hence:

x + 116 = 180

x = 64°

The value of x in the straight line shown in the attached diagram is 64°

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The distance between points M and N according to the task content is; 9.8 meters.

From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints of KL and JL respectively.

Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;

NM/19.6 = 7.4/(2×7.4)

NM = 19.6/2 = 9.8 meters.

This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.

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Answer: 9.8 meters

Step-by-step explanation:  Trust Me!! I got the answer correct on Edge.

Q:  What is the distance between points M and N?

A:  9.8 meters  

The amount Cindy should increase in each dimension of the scaled model is 12 m.  

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

We have:

The scaled model of the container has dimensions 2m by 4m by 6m.

Volume of the scaled model = 2×4×6 = 48 cubic m

Let x be the amount by which each dimension is increased.

(2 + x)(4 + x)(6 + x) = 84(48)

[tex]\rm 48+44x+12x^2+x^3=4032[/tex]

[tex]\rm x^3+12x^2+44x-3984=0[/tex]

[tex]\rm x-12=0\quad \mathrm{or}\quad \:x^2+24x+332=0[/tex]

The quadratic equation has no real solution so,

x = 12 m

Thus, the amount Cindy should increase in each dimension of the scaled model is 12 m.  

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A characteristic of a simple random sample is that all samples of the same population have an equal chance to be selected.

A subset of a statistical population called a simple random sample is one in which each member has the same chance of being picked or selected.

A subset of participants is chosen at random by the researcher using this sampling approach from a population.

To make sure that the sample represents the population, simple random sampling is often performed and this technique helps to sample bigger populations more frequently than smaller subpopulations.

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The probability that the team will win the sport is 77%.

Given that an area kicker in pro football incorporates a 77% probability of creating a field goal over 40 yards and every attempt field goal is independent.

Probability is how something is likely to happen. The probability of a happening is calculated by the probability formula by simply dividing the favorable number of outcomes by the overall number of possible outcomes.

So, his team will win the sport if he makes a goal otherwise loses.

Therefore, the Probability that his team will win the sport P[E] =P[making a field goal]

P[E]=77%

Hence, the probability that the team will win the sport when making a field goal is 77%.

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Answer:

it might be greater i think

The expected value after 10 game at a carnival is 16.1 tickets.

Given the probabilities that bag lands into the outer ring, middle ring, center are 0.64, 0.11 and remaining. 1 ticket awarded for the outer, 2 for middle and 3 for middle.

We have to find the expected value we will get if we play the game 10 times.

Probability is the chance of happening an event among all the events possible. Value of probability lies between 0 and 1. The formula of probability is as under:

Probability=number of items/ total items in consideration.

Probability that bag lands in center is 1-0.64-0.11=0.25.

Expected value when game is played 1 time=1*0.64+2*0.11+3*0.25

=0.64+0.22+0.75

=1.61

Expected value when the game is played 10 times=10*1.61

=16.1 tickets.

Hence the expected value when game is played 10 times is 16.1 tickets.

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In analyzing Manda’s work, she made a mistake instep 3, she did not subtract one x from the left side.

Fractions are known to be the parts of a complete or whole numbers of objects. It is known to have a numerator and a denominator and when solving for it, the rule of BODMAS must be obeyed.

In step 3 we see that (image attached)  she did not subtract one x from the left side. The right thing to do is to use x to cancel out on the both side and that will make the answer to  be correct but she did not.

So her error is seen in step 3 and as such, option C is correct.

See full question in the image attached.

Options are

Analyze Manda’s work. Is she correct? If not, what was her mistake?

A. Yes, she is correct.

B. In step 2, she needed to multiply both sides by 10.

C. In step 3, she did not subtract one x from the left side.

D. In step 4, she did not simplify her fraction.

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Using proportions, considering the given ratio, it is found that 9090 grapes were there.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The ratio of bananas to grapes of 3:101 means that out of 104 fruits, 3 are bananas and 101 are grapes. Hence the rule of three is given as follows:

3 bananas - 101 grapes

270 bananas - n grapes.

Applying cross multiplication:

3n = 101 x 270

n = 101 x 270/3

n = 9090.

9090 grapes were there.

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[tex] \sf{\red{Answer}}[/tex]

[tex]\sf{m = \frac{1}{2} }[/tex]

[tex] \sf{\purple{Explanation}}[/tex]

[tex] \sf{m = \frac{y_{2}- y_{1}}{m_{2} - m_{1}} }[/tex]

[tex] \sf{m = \frac{9- 3}{7- ( - 5)} }[/tex]

[tex]\sf{m = \frac{6}{7 + 5} }[/tex]

[tex]\sf{m = \frac{6}{12} }[/tex]

[tex]\sf{m = \frac{1}{2} }[/tex]

Answer:

The order of operations is Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

Step-by-step explanation:

The order of operations is PEMDAS.

P: Parenthesis

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

An easy way to remember PEMDAS is, please excuse my dear aunt sally.

Hope this helps!

If not, I am sorry.

Answer:

0y^2 + 2z^3 + 3y^3

Step-by-step explanation:

The simplified form of the expression is 0y²+2z³ + 3y³

The given expression is -1/3y² + 2/3 z³ +1/3y² +3y³+4/3z³.

In the expression y, z are the variables.

Combine the like terms:

(-1/3+1/3)y²+(2/3+4/3)z³ + 3y³

Simplify each term:

0y²+2z³ + 3y³

Hence, the simplified form of the expression is 0y²+2z³ + 3y³

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Answer:

<PQR is 130 degrees

Step-by-step explanation:

When it says the line bisects the angle, that means the two smaller angles are equal to each other.

Therefore 3x+5 = 2x+25

Now rearrange to get x.

3x-2x=25-5

x=20

Now plug the x back into both phrases and them together to get the final answer for <PQR.

20 * 3 + 5 = 65

20 * 2 + 25 = 65

65*2 = 130

Answer: x > -1, see attached.

Step-by-step explanation:

To solve the inequality, we will isolate the x-variable.

Given:

    3x - 19 > -22

Add 19 to both sides:

    3x > -3

Divide both sides by 3:

    x > -1

To graph, we will use an open circle since it is only greater than and not equal to. Then, we will place this circle on -1. Lastly, we will shade to the right of -1, since it is greater than -1.

Answer:

(a) 1

(b) 1/2

(c) 1/2

Step-by-step explanation:

[tex]x^2 + y^2 = 5/8 (1)\\\frac{4}{3}xy = \frac{1}{4} (2)\\\\\textrm {From (2) by multiplying both sides by 3/4 we get}\\\\xy = \frac{3}{16} (3)\\\textrm{We know that } (x + y)^2 = x^2 + 2xy + y^2 \\\textrm{Adding 2xy to the LHS and RHS of equation 1 gisues us }\\x^2 + y^2 + 2xy = \frac{5}{8} + 2 * \frac{3}{16} = \frac{5}{8} + \frac{3}{8} = \frac{8}{8} = 1[/tex]

[tex](x + y)^2 = 1 == > x+y = \sqrt{1} = 1\\\\(x - y)^2 = x^2 -2xy + y^2\\\\\textrm{Subtracting 2xy from both sides of Equation 1}\\x^2 + y^2 - 2xy = \frac{5}{8} - 2*\frac{3}{16} = \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \\x-y = \sqrt{\frac{1}{4}} = \frac{1}{2}\\\\x^2 - y^2 = (x+y)(x-y) = 1 . \frac{1}{2} = \frac{1}{2}[/tex]

The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the markup, since the store sells the cell phone for $315, hence:

(315 - 140)/140 * 100% = x

x = 125%

The store bought the phone for $140 and sells the cell phone for $315 at a markup of 125%.

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