Use graphing technology to approximate the solutions of the equation. x2 + 5x - 12 = | x + 3| + 7

Answer:

0.0428 miles per gallon

Step-by-step explanation:

On her vacation in Mexico Stephanie was Abel to drive 280 miles on 12 gallons

Given data

Distance driven = 280miles

Fuel used= 12 gallons

Hence the gas per mile is expressed as

Gas per mile= 12/280

Gas per mile= 0.0428 miles per gallon

Answer:

Add 7 to both sides

Step-by-step explanation:

The equation has to be just x = y

There cannot be another number on the same side as the variable

Now that we did that, the equation is 9x = 0

x = 0

Well, that was easy lol

Answer:

Step-by-step explanation:

Add 7 to both sides

9x = 0

Then divide by 9 both sides to get x by itself

x = 0

Usando la tasa conjunta, se encuentra que se tardaría 2.4 horas en llenarse la piscina con los dos grifos a la vez.

La tasa conjunta es la suma de cada tasa por separado.

En este problemas, las tasas por separadas són dadas por 1/6 y 1/4. Por eso, la tasa conjunta es dada por:

\(\frac{1}{x} = \frac{1}{6} + \frac{1}{4}\)

\(\frac{1}{x} = \frac{2 + 3}{12}\)

\(\frac{1}{x} = \frac{5}{12}\)

\(5x = 12\)

\(x = 2.4\)

Se tardaría 2.4 horas en llenarse la piscina con los dos grifos a la vez.

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Answer:

750

Step-by-step explanation:

15000 x .05 = 750  5% as a decimal is .05

Answer:

9 containers

Step-by-step explanation:

Given

Total pounds of potato salad = 11 1/2 pounds

If one container holds 1 1/4 pounds:

The number of container that 11 1/2 pounds can hold is expressed as:

Number of container = Total pounds/volume of one container

Number of container = 11 1/2 ÷ 1 1/4

Convert to improper fraction

Number of container = 23/2 ÷ 5/4

Number of container = 23/2 × 4/5

Number of container = 92/10

Number of container = 9.2

Therefore she will need 9 containers

Answer:

Like terms would be option B   variables and different exponents.

Answer:

the answer is b

Step-by-step explanation:

just turn the 4/5 to 5/4

Answer:

D. This is impossible.

Step-by-step explanation:

4/5 x 7 or 0.8 x 7 = 5.6

None of the answers equal this same amount when replacing K x L. Plus, B and C are the same, since when multiplying, you can multiply in any order. A does not equal this amount either.

Hope this helps! :)

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

Answer:

Circumference of a cicle in terms of radius:

Circumference = 2·π·r = 2·3.14·3 = 18.85(*)

In terms of diameter:

Circumference = π·d = 3.14·6 = 18.84(*)

In terms of area:

Circumference C = √4·π·A = √4·π·28.27 =18.85

Step-by-step explanation:

radius= 3in.

the circumference of the circle.

formula C=2πr

=2·π·3

≈18.84956in

nearest hundredth= 18.85in

Answer:

4^4×6^2

Step-by-step explanation:

There are four 4's and two 6's

So in exponential form it is 4^4×6^2

Answer:

15

Step-by-step explanation:

x - y = 10, then x = 10 + y

x + y = 20

substitute for x:

10 + y + y = 20

2y = 10

y = 5

x = 10 + 5 = 15

The chemical formula for ammonium carbonate is (NH₄)₂CO₃. Therefore, option (C) is correct.

When heated, ammonium carbonate, also known as ()2, rapidly breaks down into ammonia and carbon dioxide. It functions as a smelling salt and a leavening agent. Ammonium carbonate, often known as baker's ammonia, was used before baking soda and baking powder as leaveners.

Sal volatile contains ammonium carbonate, and salt of hartshorn when baked emits a strong odour. At standard pressure and temperature, two processes lead to the gradual breakdown of ammonium carbonate. The pure ammonium carbonate sample will combine with different byproducts.

Upon spontaneous dissociation, ammonium carbonate can separate into ammonium bicarbonate and ammonia. which results in the addition of more ammonia, carbon dioxide, and water.

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Answer:

The formula for the ammonium ion: NH4+

The formula for the nitrate ion: NO3–  

A chromate ion consists of four oxygen atoms bonded to a chromium atom. It has two extra electrons. The formula of this ion: CrO42–

Heres all three. Hope i helped

Answer:

212 bp^3 (base pairs cubed) - 121 bp^3 (base pairs cubed) + 222 bp^3 (base pairs cubed) = 313 bp^3 (base pairs cubed

Step-by-step explanation:

Given:

The figure of two quadrilaterals.

In \(ABCD,AB=18,BC=20,CD=22,AD=24\)

In \(EFGH,EF=27,FG=30,GH=34, EH=36\)

To find:

Whether the figures are congruent, similar or neither.

Solution:

Ratio of corresponding sides are:

\(\dfrac{AB}{EF}=\dfrac{18}{27}\)

\(\dfrac{AB}{EF}=\dfrac{2}{3}\)

Similarly,

\(\dfrac{BC}{FG}=\dfrac{20}{30}\)

\(\dfrac{BC}{FG}=\dfrac{2}{3}\)

\(\dfrac{CD}{GH}=\dfrac{22}{34}\)

\(\dfrac{CD}{GH}=\dfrac{11}{17}\)

And,

\(\dfrac{AD}{EH}=\dfrac{24}{36}\)

\(\dfrac{AD}{EH}=\dfrac{2}{3}\)

Clearly, \(\dfrac{AB}{EF}=\dfrac{BC}{FG}=\dfrac{AD}{EH}\neq \dfrac{CD}{GH}\).

All corresponding sides are not proportional.

Therefore, the figures are neither similar nor congruent. Hence, third option is correct.

Answer:

Since your diameter is 8,

half of that is 4.

We are going to find the area now of both the bottom and the top.

4^4 = 16

16 x 3.14 = 50.24

Now we multiply by two since there are two circles  (bottom and top) we only got one circle's area.

50.24 x 2 = 100.48

Now we need to find the round curved area.

In order to do that we need to find the circumference them multiply by the height:

2 x 3.14 x 4 = 25.12(circumference)

25.12 x 19Height) = 477.28

Now we need to add both the areas(surface area):

477.28 + 100.48 = 577.76 yard2 is your answer.

Answer:

Because of cars, and factories making it everyday.

Step-by-step explanation:

Answer:-7/31

Step-by-step explanation:

Answer:

x<24

*the answer will be incorrect if you meant 2/(3x) instead of (2/3)x

Step-by-step explanation:

First, add 7 to both sides of the inequality to get "2/3x<16." Then multiply both sides by 3 to get "2x<48." Finally, divide both sides by 2 to get "x<24"

Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

▪︎▪︎▪︎▪︎▪︎▪︎

Answer:

\(\sqrt{2\left(4+\sqrt{15}\right)}\)

Step-by-step explanation:

\(\sqrt{8+2\sqrt{15}}\)

Factorize

\(=\sqrt{2\left(4+\sqrt{15}\right)}\)

(a) If 3^(2k) - 5 is divisible by 4, then 3^(2(k+1)) - 5 is also divisible by 4. By the principle of mathematical induction, we conclude that 3^(2n) - 5 is divisible by 4 for all n ∈ N. (b) If 9^m = 8k + 1, then 9^(m+1) = 8p + 1. By direct proof, we can conclude that 9^n is always one more than a multiple of 8 for all n ∈ N.

In part a, we need to prove by induction that 3^(2n) - 5 is divisible by 4 for all n ∈ N.

To prove this, we will use mathematical induction.

Base Case: For n = 1, we have 3^(2(1)) - 5 = 9 - 5 = 4, which is divisible by 4.

Inductive Step: Assume that 3^(2k) - 5 is divisible by 4 for some arbitrary positive integer k. We need to prove that 3^(2(k+1)) - 5 is also divisible by 4.

Starting with the left-hand side, we have 3^(2(k+1)) - 5 = 3^(2k + 2) - 5 = 9(3^(2k)) - 5 = 9(3^(2k) - 5) + 40.

Since we assumed that 3^(2k) - 5 is divisible by 4, let's say it is equal to 4m for some integer m. Then, we can rewrite the expression as 9(4m) + 40 = 36m + 40.

Now, we need to show that 36m + 40 is divisible by 4. Dividing this expression by 4 gives us 9m + 10. Since 9m is divisible by 4, the remainder is 10.

In part b, we are asked to prove directly that 9^n is one more than a multiple of 8, i.e., 9^n = 8k + 1 for some k ∈ N.

To prove this, we can use a direct proof. Let's consider the base case: for n = 1, we have 9^1 = 9 = 8(1) + 1, which satisfies the given condition.

Now, let's assume that for some arbitrary positive integer m, 9^m = 8k + 1 for some k ∈ N. We need to show that 9^(m+1) = 8p + 1 for some p ∈ N.

Starting with the left-hand side, we have 9^(m+1) = 9^m * 9. By our assumption, we can substitute 9^m with 8k + 1, giving us (8k + 1) * 9 = 72k + 9 = 8(9k + 1) + 1.

Since 9k + 1 is an integer, let's call it p.

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The correct answer is A. The selling price of a bond is affected by the coupon rate and the market interest rate.

If the coupon rate is less than the market interest rate, investors will not be interested in buying the bond because they can get a higher return elsewhere. This results in the selling price of the bond being less than its face value of $10,000.
The selling price of a $10,000 5-year bond will be less than $10,000 if the:
A. Coupon rate is less than the market interest rate

This is because when the coupon rate (the interest paid by the bond) is lower than the market interest rate, investors would prefer to invest in other options that offer a higher return. Therefore, to attract buyers, the bond's selling price would be discounted to compensate for the lower coupon rate.

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If Ahmad works at a constant rate, he will take 90 minutes in finishing his exam, and he will finish it at around 1:15 pm.

We know that Ahmad answers at a constant rate, and he takes around 1.5 minutes to answer each answer.

The total time that it will take him to answer the 60 questions is equal to the number of questions times the time that it took him to answer each one, then the total time is:

T = (1.5 min)*60  = 90 minutes

So it will take him an hour and a half.

And e know that the exam starts at 11:45 am

After one hour, it will be:

0:45 pm

And after 30 minutes, it will be:

1:15 pm

Ahmad will finish his exam at 1:15 pm.

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Answer:

8n+7

Step-by-step explanation:

Growth rate

\(\\ \sf\longmapsto Distance/Time\)

\(\\ \sf\longmapsto 6/12\)

\(\\ \sf\longmapsto 0.5in/h\)

To calculate the chances of success for each student, the school would likely use logistic regression analysis.

Logistic regression analysis is a statistical technique used to model the relationship between a binary outcome variable (in this case, success or failure) and one or more predictor variables (such as academic performance, attendance, or socio-economic factors). The goal of logistic regression is to estimate the probability of a specific outcome occurring based on the given predictors. In this scenario, the school would be interested in determining the likelihood of success for each student based on various factors. Logistic regression allows for the calculation of the probability of success and can provide insights into the factors that significantly contribute to or hinder student success. By analyzing the relationship between the predictor variables and the binary outcome of success, the school can gain valuable information to make informed decisions and interventions to support student achievement.

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Applying the midpoint formula, the coordinates of the other endpoint are: (-9, -13).

The midpoint formula, which can be used in determining the coordinates of the midpoint between two endpoints is usually expressed as: M[(x1 + x2)/2, (y1 + y2)/2].

Given the following coordinates:

Midpoint of GH --> m(-13/2,-6) = (x, y)

One endpoint ---> G(-4, 1) = (x1, y1)

The other endpoint ---> (x2, y2)

Plug in the values into the formula used in calculating the midpoint:

m(-13/2,-6) = [(-4 + x2)/2, (1 + y2)/2]

Solve for x2

-13/2 = (-4 + x2)/2

-13/2 × 2 = -4 + x2

-13 = -4 + x2

-13 + 4 = x2

-9 = x2

x2 = -9

Solve for y2

-6 = (1 + y2)/2

2(-6) = 1 + y2

-12 = 1 + y2

-12 - 1 = y2

-13 = y2

y2 = -13

Thus, using the midpoint formula, the coordinates of the other endpoint are: (-9, -13).

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Answer:

a) P(t) = 5/6t + 20

b) 34.2 beetles

c) After 78 weeks.

Step-by-step explanation:

a) A general linear growth model can be expressed as P(t) = at + b, where P is the number of beetles in time t and t is the time in weeks.

It is known that:

P(0) = 20

P(6) = 25

These values can be substituted in the general equation to find a and b:

P(t) = at + b

P(0) = 20:

20 = a*0 + b

20 = 0 + b

20 = b

So,

P(t) = at + 20

Using P(6) = 25:

25 = a*6 + 20

25 - 20 = a*6

5 = a*6

5/6 = a

So, the linear growth model can the represented as:

P(t) = 5/6t + 20

b)

The number of beetles after 17 weeks is P(17):

P(17) = 5/6*17 + 20

P(17) = 14.1 + 20

P(17) = 34.2

34.2 beetles.

c)

P(t) = 85

85 = 5/6t + 20

85 - 20 = 5/6t

65 = 5/6t

t = 65*6/5

t = 78

After 78 weeks.

Answer:

B=12.2

C=5.4 is your answer