standard form of x^2 + 16x + 71

Answer:

Steve's temperature now is 99 degrees.

Step-by-step explanation:

102 degrees- 3 degrees=

99 degrees.

Steve's temperature was 102º F when he woke up. Two hours later, his temperature had dropped by 3º F, thus making his temperature 99º F.

The subject of this question is a real-life mathematics reasoning task about temperature change. Based on the given information, Steve's initial temperature when he woke up was 102º F.

According to the problem, Steve's temperature decreased by 3º after two hours.

To find Steve's temperature after the decrease, you simply have to subtract this decrease from the original temperature. So you calculate 102º F - 3º F, which equals 99º F. Therefore, Steve's temperature two hours later was 99º F.

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Answer:

No.

Step-by-step explanation:

If it is geometric  the quotient of the terms and the previous term will be a constant.

213 / 31 = 6.871

4459 / 213= 20.93

These are not equal so the sequence is not geometric.

Step-by-step explanation:

Part A:

Let [tex]m[/tex] be the number of mittens and [tex]s[/tex] be the number of scarves. Then we have the inequalities:

[tex]s+m\leq 30.[/tex] This says Nivyana and Ana cannot make more than 30 scarves

[tex]50s+25m\geq 1000.[/tex] This says that Nivyana and Ana have to earn at least $1000.

Part B:

The graph is attached.

Notice that the graphs of the inequalities are solid lines, this just means that the points on these lines included to the solutions of each inequality.

The darker shaded region and the solid lines bounding it, are the solutions to the inequalities because that's where the values common to both inequalities are found.

Part C:

From the graph we get two possible solutions:

15 scarves & 10 mittens

25 scarves & 5 mittens.

These two points lie on the solid lines that bound the darker shaded region (I picked those points to stress that the lines bounding the dark region are also solutions.)

Final answer:

To find the product of the given expression (7x²)(2x + 5)(x² - 4x-9), we can use the distributive property to multiply each term.

Explanation:

To find the product of the given expression (7x²)(2x + 5)(x² - 4x-9), we can use the distributive property to multiply each term.

First, multiply (2x + 5) with (x² - 4x-9) using the distributive property.
(2x + 5)(x² - 4x-9) = 2x*(x² - 4x-9) + 5*(x² - 4x-9)
= 2x³ - 8x² - 18x + 5x² - 20x-45
= 2x³ - 3x² - 38x - 45

Answer:

[tex]14 \frac{3}{8}[/tex]

Step-by-step explanation:

I assume you mean this:

[tex]8 \frac{7}{8} +(7 \frac{5}{6} -2\frac{1}{3} )[/tex]

Lets begin with the parentheses. When operating with fractions, we need them to have the same denominator. Looking at the expression in the parenthesis, we can see that the denominator of 5/6, that being 6, is twice that of 1/3, that being 3. Thus, if we multiply the numerator and denominator of 1/3 by 2, the result will be a fraction of same value, but with denominator 6, which we can work with.

[tex]\frac{1*2}{3*2}[/tex]

[tex]\frac{2}{6}[/tex]

Now we can replace this in the original parenthesis

[tex](7 \frac{5}{6} -2\frac{2}{6})[/tex]

We can now evaluate the parenthesis. 7-2=5, which leaves us with 5 5/6 - 2/6. Since the two fractions have the same denominator, we can subtract the numerator of 2/6 from 5/6. This gives us with 3/6, which we add to the 5 from before.

[tex]5\frac{3}{6}[/tex]

The numerator and denominator of 3/6 are both divisible by three, so we can simply the fraction.

[tex]5\frac{1}{2}[/tex]

Now that we have solved the parenthesis, we can plug our solution back into the original expression.

[tex]8 \frac{7}{8} +5\frac{1}{2}[/tex]

We now have a similar problem to the parenthesis, where our fractions have different denominators. However, you may notice that the denominator of 7/8 (8) is four times larger than the denominator of 1/2 (2). Thus, if we multiply the numerator and denominator of 1/2 by four, we will have a new fraction of equal value, but with denominator 8.

[tex]\frac{1*4}{2*4}[/tex]

[tex]\frac{4}{8}[/tex]

Now lets update our expression with this information.

[tex]8 \frac{7}{8} +5 \frac{4}{8}[/tex]

8+5=13[tex]13\frac{7}{8} +\frac{4}{8}[/tex], so we can further simplify the expression.

Since the denominators of the fractions are the same, we can combine the numerators. 7+4=11

[tex]13 \frac{11}{8}[/tex]

We can simplify the fraction by taking one whole out of it (8/8) and adding it as 1 instead. 11-8=3, thus the fraction that remains is 3/8.

[tex]14 \frac{3}{8}[/tex]

The operation 8 7/8+(7 5/6-2 1/3) evaluates to a final result of 14 3/8.

To evaluate this mixed number operation, we must first convert each mixed number into an improper fraction.

8 7/8 is the same as 71/8 and 7 5/6 as 47/6 and 2 1/3 as 7/3.

Now, conduct the operation inside the parenthesis, which is subtraction: 47/6 - 7/3.

To subtract fractions, they must have the same denominator. Here, the least common multiple of 3 and 6 is 6. So you have 47/6 - 14/6 equals 33/6 reduced to 5 1/2.

Then add this quantity to 8 7/8 which equals to 14 3/8 when converted to a mixed number.

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Answer: -2n + -18

Explanation: Let's simplify this problem using the distributive property.

The first thing we want to do is to distribute or multiply the -2 by each of the terms inside the set of parentheses.

So we get -2 (n) + -2 (9) and this simplifies to -2n + -18.

Answer:

(1, -3)

Step-by-step explanation:

Solve the system of equations of the two lines:

10x-3y=19 ------> eq 1

5x+4y=-7 --------> eq 2

Solve by elimination:

eq 2 x 2

2( 5x+4y) = 2(-7 )

10x + 8y = - 14 ------> eq 3

eq3 - eq 1:

(10x + 8y) - (10x-3y) = - 14 - 19

10x + 8y - 10x + 3y = -33

8y + 3y = -33

11y = -33

y = -3  (substitute back into eq 1)

10x - 3y = 19

10x - 3(-3) = 19

10x + 9 = 19

10x  = 19 - 9

10x = 10

x = 1

Hence the intersection point is (1, -3)

C. 2.3 miles

Step-by-step explanation:

The details of the image are as follows;

Ranger station to Nature Center = 90°

Nature center to petting zoo= 40°

Petting zoo to Tennis court =120°

Tennis court to Pool = 65°

Pool to Ranger station= 45°

The radius of the circular pattern = 1 mile

The formula to apply is;

Arc length = 2πr angle / 360° where r is radius and π=3.14

Finding arc length from Ranger Station to Nature Center will be;

Arc length = 2×3.14×1×90°/360°

Arc length=2×3.14×1×1/4 =1.57 miles

Finding distance from Nature Center to Petting Zoo

Arc length= 2×3.14×1×40°/360°

Arc length= 2×3.14×1×1/9 = 0.70 miles

Total =1.57+0.70 =2.27 miles

Answer to the nearest hundredth = 2.3 miles

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Answer:

32

Step-by-step explanation:

Subtract 4 from 100

96

Divide by 3

32

The solution to the equation is x = 32, so Elijah baked 32 brownies last week.

To find out how many brownies Elijah baked last week, we need to solve the equation 100 = 4 + 3x, where x is the number of brownies he made last week. Here are the steps to solve the equation:

Therefore, Elijah baked 32 brownies last week.

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Answer:

The theorem states that if a right triangle has two sides equal to a and b, and a hypotenuse equal to c, then a squared plus b squared equals c squared. The hypotenuse of a right triangle is the side opposite the right angle.

Step-by-step explanation:

Answer: 3,000

Step-by-step explanation:

Divide 48,000 by 16

48,000 ÷ 16 = 3,000

Answer:

3000

Step-by-step explanation:

If they produce 48,000 in 16 hours, that means in one hour they produce 48,000 divided by 16.

48000 ÷ 16 = 3000

Answer:

The correct option is

The origin is included in the shaded region and the shaded area is below the line.

Step-by-step explanation:

Y>3/2x + 2

Put x=0

Y= 2

(0,2)

Put y=0

X= -4/3

(-4/3,0)

See attached picture for the sketch

Answer:

The origin is included in the shaded region and the shaded area is below the line.

The slope of 0.5 represents the cost per additional topping, while the y-intercept of 5 represents the cost of the plain pizza. Option A provides the correct interpretations.

To interpret the slope and y-intercept of the equation C = 0.5m + 5, where  C  represents the cost of the pizza and m represents the number of additional toppings:

A. The correct interpretation is:

- Slope: The slope of 0.5 represents the cost per additional topping. This means that for each additional topping added to the pizza, the cost increases by $0.5.  

- Y-intercept: The y-intercept of 5 represents the cost of the plain pizza without any additional toppings. This is because when m = 0 (no additional toppings), the cost of the pizza is $5, which is the flat fee for the plain cheese pizza.

To confirm:

- When m = 0, the equation becomes C = 0.5(0) + 5 = 5 , which is the cost of the plain pizza without any additional toppings.

- When m = 1, the equation becomes C = 0.5(1) + 5 = 5.5, indicating that the cost increases by $0.5 when one additional topping is added.

Therefore, option A correctly interprets the slope and y-intercept of the equation.

Answer:

C

Step-by-step explanation:

The slope is 4/1, written as 4

The y int is 4

Write the equation in y = mx + b form

y = 4x + 4

Option C

Total amount paid by Alberto is $ 1745.7

Given that Alberto paid for seven large tables to be delivered to the restaurant

Alberto paid a delivery fee of  $95.45

Cost of 1 table = $ 235.75

To find: total amount Alberto paid

cost of seven tables = cost of 1 table x 7

[tex]\text {cost of seven tables }=235.75 \times 7=1650.25[/tex]

Total amount paid = 1650.25 + 95.45

Total amount paid = 1745.7

Thus total amount paid by Alberto is $ 1745.7 Therefore option C is correct

Answer:

[tex]x=30^o[/tex]

Step-by-step explanation:

step 1

Find the measure of angle KNL

we know that

[tex]m\angle KNL+m\angle LNM+m\angle ONM=180^o[/tex]----> by straight angle

we have

[tex]m\angle LNM=45^o[/tex] ---> given problem

[tex]m\angle ONM=105^o[/tex] ---> given problem

substitute the given values

[tex]m\angle KNL+45^o+105^o=180^o[/tex]

[tex]m\angle KNL+150^o=180^o[/tex]

[tex]m\angle KNL=180^o-150^o[/tex]

[tex]m\angle KNL=30^o[/tex]

step 2

Find the value of x

In the right triangle KNL

we know that

[tex]m\angle KNL+m\angle NKL=90^o[/tex] ----> by complementary angles

we have

[tex]m\angle KNL=30^o[/tex]

[tex]m\angle NKL=2x[/tex]

substitute

[tex]30^o+2x=90^o[/tex]

[tex]2x=90^o-30^o[/tex]

[tex]2x=60^o[/tex]

[tex]x=30^o[/tex]

Step-by-step explanation:

[tex]28\cdot\dfrac{4}{7}=\dfrac{28}{1}\cdot\dfrac{4}{7}=\dfrac{28\cdot4}{1\cdot7}\\\\\text{simplify 28 and 7 (divide both by 7)}\\\\=\dfrac{28\!\!\!\!\!\diagup^4\cdot4}{1\cdot7\!\!\!\!\diagup_1}=\dfrac{4\cdo4}{1\cdot1}=\dfrac{16}{1}=16[/tex]

[tex]\dfrac{28}{7}\cdot4=(28:7)\cdot4=4\cdot4=16[/tex]

[tex]\text{Both expressions give the same result.}[/tex]

[tex]28\cdot\dfrac{4}{7}=\dfrac{28}{7}\cdot4\\\\28\cdot\dfrac{4}{7}=\dfrac{28}{1}\cdot\dfrac{4}{7}=\dfrac{28\cdot4}{1\cdot7}=\dfrac{28\cdot4}{7\cdot1}=\dfrac{28}{7}\cdot\dfrac{4}{1}=\dfrac{28}{4}\cdot4[/tex]

Your question:

EXPLAIN HOW 28*4/7 IS CORRECT AND (28 / 7) x 4 IS NOT

It all depends on the content of the question for which these expressions are.

Qestion:

Mr. Chang’s class has 28 students, 4/7 of whom are girls. Which equation shows how to determine the number of girls in Mr. Chang’s class?

Correct is 28 * 4/7.

(You calculate a fraction of a number).

28/7 * 4 - gives the same result. But the expression does not match the content of the question.

Answer: 12 gallons

Step-by-step explanation:

Use proportion to estimate how much gas she needs for 204 miles.

10:120=x:204

204*10=120x

x=2040/120

x=17 gallons

For 204 mile trip Trina needs 17 gallons of gas. She has 5 gallons.

17-5=12

She will need 12 gallons of gas.

Answer:15/28

Step-by-step explanation: Ive had this question before That is the answer :)

Final answer:

To find the probability of selecting a solid sock both times from Daniel's drawer, multiply the probabilities at each step independently to get 1/105 or approximately 1% in total.

Explanation:

To calculate the probability of selecting a solid sock both times, you need to consider the independent probabilities at each step.

Probability of selecting a solid sock the first time is 1/7.

Probability of selecting a match for the second sock from the remaining socks would be 1/5.

Continuing this pattern, the total probability of selecting a solid sock both times is 1/105 or about 1%.

Answer:

∠Q = 75 °

Step-by-step explanation:

Since PR = PQ then Δ PQR is isosceles and the base angles are congruent, that is

∠R = ∠Q = 2x + 15

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

2x + 15 + 2x + 15 + x = 180, that is

5x + 30 = 180 ( subtract 30 from both sides )

5x = 150 ( divide both sides by 5 )

x = 30

Hence

∠Q = 2x + 15 = (2 × 30) + 15 = 60 + 15 = 75°

Answer:

If X is the starting weight, total pounds lost in three months is

(0.132X + 2.37)lbs

Step-by-step explanation:

Let the starting weight be X(lb)

Let the target ending weight be Y(lb)

Since Rollie ended with 3(lbs) above goal weight, final weight is Y+3(lb)

Each month, Rollie lost 1/3 of the difference between current weight and goal weight, hence

In the first month, Rollie lost 1/3 of (X - Y)

but since Rollie ended up with 3lbs above target ending weight, the actual weight loss is 1/3(X - Y) + 3

Hence  by the end of the first month, Rollie's new weight is X - (1/3(X - Y)) + 3

which is equal to

X - 1/3X + 1/3Y - 3.

= 2/3X + 1/3Y - 3

By the second month, Rollie's starting weight is 2/3X + 1/3Y - 3(lb)

while her target ending weight still remains (Y)

but the actual ending weight is Y + 3

hence in the second month, Rollie lost 1/3(2/3X + 1/3Y - 3 - Y) + 3

= 2/9X + 1/9Y - 1 - 1/3Y + 3

=  2/9X - 2/9Y + 2

hence by the end of the second month, Rollie's new weight is

(2/3X + 1/3Y - 3) - (2/9X - 2/9Y + 2)

= 2/3X - 2/9X + 1/3Y + 2/9Y - 3 - 2

= 4/9X + 5/9Y - 5  

By the third month, Rollie's starting weight is 4/9X + 5/9Y - 5(lb)

while her target ending weight still remains (Y)

but the actual ending weight is Y + 3

hence in the third month, Rollie lost 1/3(4/9X + 5/9Y - 5 - Y) + 3

= 4/27X + 5/27Y - 5/3 - 1/3Y + 3

= 4/27X - 4/27Y + 4/3 ------------------------- eqn (*)

hence by the end of the third month, Rollie's new weight is

(4/9X + 5/9Y - 5) - (4/27X - 4/27Y + 4/3)

= 4/9X - 4/27X + 5/9Y + 4/27Y - 5 - 4/3

= 8/27X - 19/27Y - 19/3

Hence in three months, Rollie's new weight is 8/27X - 19/27Y - 19/3

To ascertain how much weight Rollie lost in three months, there is need to equate the estimated ending weight to the final weight (Y + 3)

Therefore:

8/27X - 19/27Y - 19/3 = Y + 3

this implies that

8/27X - 19/27Y - Y - 19/3 - 3 = 0

8/27X - 36/27Y -28/3 = 0

Since Y is the target ending weight

the ending weight is generated by solving the equation with respect to Y

36/27Y = 8/27X - 28/3

multiply through by 27/36

Y = 2/9X - 7

Hence weight lost in three months is generated by substituting for Y = 2/9X - 7  in eqn (*)

Since eqn * is 4/27X - 4/27Y + 4/3

the lbs lost in three months is

4/27X - 4/27(2/9X - 7 ) + 4/3

= 4/27X - 8/243X + 28/27 + 4/3

= (32/243)X + 64/27

which in decimal is

(0.132X + 2.37)lbs

The total pounds of weight that will be lost in three months will be (0.132x + 2.37)lbs.

The starting weight is illustrated by x. The target ending weight is illustrated by y.

In the first month, the weight list by Rollie will be 1/3 × (x - y) and her new weight will be:

= 2/3x + 1/3y - 3

In the second month, the starting weight will be 2/3x + 1/3y - 3. The weight lost by the end of the second month will be:

= 1/3 × (2/3x + 1/3y - 3) + 3

= 2/9x - 2/9y + 2

The new weight will be:

= (2/3x + 1/3y - 3) - (2/9x - 2/9y + 2)

= 4/9x + 5/9y - 5

In conclusion, the weight lost in three months will be:

= 4/27x - 4/27(2/9x - 7) + 4/3

= 4/27x - 8/243x + 28/27 + 4/3

= 32/343x + 64/27

= 0.132x + 2.37

In conclusion, the total pounds of weight that will be lost in three months will be (0.132x + 2.37)lbs.

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Answer:

y = 3

Step-by-step explanation:

Given:

x²+y²+3xy =-5  and x = -2

Substituting x=-2 into the equation:

(-2)² + y² + 3y(-2) = -5

4 + y² - 6y = -5

y² - 6y +4 + 5 = 0

y² - 6y +9  = 0   (solve by factorization)

(y-3) (y-3) = 0

y = 3

Answer:

y = 5x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 5, thus

y = 5x + c ← is the partial equation

To find c substitute (2, 6) into the partial equation

6 = 10 + c ⇒ c = 6 - 10 = - 4

y = 5x - 4 ← equation of line

The markup percentage is 45.14%

Step-by-step explanation:

The given is:

We need to find the markup percentage

The markup percentage = [tex]\frac{New-Old}{old}[/tex] × 100%

∵ The selling price of a box of crackers is $1.75

∴ Old = 1.75

∵ You mark the crackers up to $2.54

∴ New = 2.54

- Substitute these values in the rule above

∵ The markup percentage = [tex]\frac{2.54-1.75}{1.75}[/tex] × 100%

∴ The markup percentage = [tex]\frac{0.79}{1.75}[/tex] × 100%

∴ The markup percentage = 0.4514 × 100%

∴ The markup percentage = 45.14%

The markup percentage is 45.14%

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Answer:

The markup percentage is 45%.

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is given that, each child bike requires 4 hours to build and each adult bike requires 6 hours to build.

Hence, c child bikes and a adult bikes require [tex](4c + 6a)[/tex] hours to build.

It is also given that, each child bike requires 4 hours to test and each adult bike requires 4 hours to test.

Total time to test, c child bikes and a adult bikes is [tex](4c + 4a)[/tex]

The company will be able to make c child bikes and a adult bikes if [tex](4c + 6a) \leq 120\\(4c + 4a)\leq 100[/tex]

If c = 20 and a = 6, then (4c + 6a) = 116 < 120.

and (4c + 4a) = 104 > 100.

Answer:

32 ounces

Step-by-step explanation:

128oz=1gal

4quarts=1gal

128÷4=32

32oz=1 quart

Answer:

1

Step-by-step explanation:

hope this helps some one

stay safe and pease still were a mask

Answer:

Step-by-step explanation:

Part A:

Let, it will take x years to pay.

According to the question,

[tex]2500\times12x = $600000 + $600000 \times \frac{3.7x}{100} \\12x = 240(1 + \frac{3.7x}{100})\\x = 2(1 + \frac{3.7x}{100})\\0.926x = 2\\x = 2.159[/tex]

Part B:

Total money that needs to be paid is [tex]600000(1 + \frac{3.7\times 2.159}{100} )[/tex] = $647929.8.

The bank made $47929.8 in profit.

Answer: $17,875

Step-by-step explanation:

take 27,500 and multiply it by 35% or .35

27500 x .35= 9625

take 9625 and subtract it from the initial value

27500 - 9625= 17875

Answer:

35 × $27500 = $9625

100 1

= $27500-$9625

=$17875

Answer:

What question? I mean all you said was 'this question' so I don't know ;-;

Step-by-step explanation:

Answer:

2.16 inches so ya

The number of inches in 15 percent of 1.2 foot is obtained as 216.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The number of inches in 1 feet = 12.

Then, in 1.2 foot the inches are 1.2 × 12 = 14.4.

Now, the percent value 15% of 1.2 foot is given as below,

15% × 1.2 foot

⇒ 15/100 × 14.4 inch

⇒ 216 inch

Hence, the number of inches are given as 216.

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