Mrs. Knight is saving money for a trip. She already has some money saved in 1 point

her savings account and will add the same amount to her account each

week. At the end of 2 weeks, she has $130. At the end of 8 weeks, she has

$280. Write a linear function to represent the amount of money (y)

Mrs. Knight has saved after x weeks

Answer:

Correct steps given below:

Ian missed the step 3 above.

He wrongly added 91 to both sides instead of subtracting, this resulted in wrong solution.

Answer:

See below.

Step-by-step explanation:

The mistake Ian made was incorrectly distributing -(-91).  When multiplying two negative numbers the result is always positive:  [tex]-a \cdot -b=-a(-b)=ab[/tex].

This error meant he added 91 to both sides of the equation in Step 3 of his calculation, when he should subtract 91 from both sides.

Therefore, the correct calculation is:

[tex]\begin{array} { r l}511 & = -7(10x-13)\\\\511 & = -70x \phantom{)))}+91\\\\-91 & \phantom{))))))))))))} -91\\\\\cline{1-2}\\420 & = -70x\\\\\dfrac{420}{-70} & = \dfrac{-70x}{-70}\\\\-6 & = x\end{array}[/tex]

The approximate solutions are -0.28 and -2.28.

Now, According to the question:

Given, the equation is 4x^2 + 3 = -12x

We have to find the approximate solutions to the equation.

Using quadratic formula,

[tex]x = \frac{-b±\sqrt{b^2-4ac} }{2a}[/tex]

The equation can be written as 4x^2 + 12x + 3 = 0.

Here, a = 4, b = 12, c = 3

x = [tex]\frac{-12±\sqrt{12^2-4(4)(3)} }{2(4)}[/tex]

x = [tex]\frac{-12±\sqrt{144-48} }{8}[/tex]

x = [tex]\frac{-12±\sqrt{96} }{8}[/tex]

x = [tex]\frac{-12±9.8}{8}[/tex]

Now, x = [tex]\frac{-12+9.8}{8} =\frac{-2.2}{8}[/tex] = -0.275

x = [tex]\frac{-12-9.8}{8} =\frac{-21.8}{8}[/tex] = -2.275

Therefore, the approximate solutions are -0.28 and -2.28.

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The complete question is this :

What are the approximate solutions of 4x^2 + 3 = -12x to the nearest hundredth?

Answer:

13.8 gallons per hour

Step-by-step explanation:

"Gallons per hour" means to divide gallons by hours.  Even the label can be a reminder of what to do:  [tex]\frac{\text{gal}}{\text{hr}}[/tex] .

Now for the math...

[tex]4\frac{5}{16} \div 1.25 =4\frac{5}{16} \div 1\frac{1}{4}[/tex]

Changing both numbers to mixed number form helps.  (You could also change both numbers to decimals--a calculator would help!)

Change mixed numbers to improper fractions, then divide.

[tex]\frac{69}{4} \div \frac{5}{4}=\\\\\frac{69}{4} \times \frac{4}{5}=\\\\\\\frac{69}{5}=13.8[/tex]

Answer:

11

Step-by-step explanation:

multiply 7 by 2, you will get 14

subtract 3 from 14 you will get 11

so the total answer is 11

According to the table the wavelength that has the least amount of electromagnetic energy is B having a wavelength of 4.0 x 10⁻⁶ m

Radiant energy that moves in waves at the speed of light is called electromagnetic energy. It can also be referred to as radiant energy, electromagnetic radiation, electromagnetic waves, light, or the movement of radiation.

Wavelength is the separation between identical points (adjacent crests) in successive cycles of a waveform signal traveling through space or over a wire.

This length is often stated in meters when using wireless technology (m),

The relationship between a electromagnetic energy and wavelength is in inverse relation. This means that the least wavelength will result to greatest electromagnetic energy

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complete question

(03.05 MC) The table below shows the wavelength of four electromagnetic waves in meters (m).

Electromagnetic Wave      Wavelength

A                                         3.0 x 10² m

B                                         4.0 x 10^-6 m

C                                         1.2 x 10-¹2 m

D                                         2.0 x 10 m

According to the table, which electromagnetic wave has the least amount of energy? ​

Answer:

Step-by-step explanation:

3.00

Answer:

1/36

Step-by-step explanation:

Since you have two six-sided die, you have 2 sets of 1-6.

Set 1: 1,2,3,4,5,6

Set 2: 1,2,3,4,5,6

Now, we need to find out how many items in the sets add up to equal a sum less than 4.

1 + 1 = 2

2 + 1 = 3

We can roll a 1 and a 1 with a 1/6 chance each.

We can also roll a 1 and a 2 with a 1/6 chance as well.

So, to get the final probability, we would multiply the two fraction together.

1/6 x 1/6 = 1/36

There is a 1/36 chance that the sum of the numbers you roll will be less than 4.

Answer:

1/36

Step-by-step explanation:

I am not a good explainer but im a genuis and when i put this as my answer for my homework i got it right

The lengths of a,b,c, and d have been derived and expressed in terms of trigonometric ratios below.

As we can see from the figure itself, the value of a = sin θ

This can be written as such because = sin θ = Perpendicular / Hypotenuse

Here, the perpendicular = a and hypotenuse = radius = 1

= sin θ = a

The value of b = tan θ

This is because tan θ = perpendicular/base

Here, the base = radius = 1

= tan θ = b  

The value of c = sec θ

This is because sec θ = Hypotenuse / Base

= sec θ = c

The value of d = cos θ

This is because cos θ = Base / Hypotenuse

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Answer:

She will buy at least 10 pounds or more.

Step-by-step explanation:

If each pound costs $4 and she is spending $40 worth, she needs to buy 10 pounds in order to spend the minimum of $40. She can buy more than 10 pounds to keep spending more money. 11, 12, 13, 14, 15, and so forth are all possible numbers in pounds she will buy.

Answer:

1,888

Step-by-step explanation:

Im pretty sure that the answer is 1,888

here is some math for it

168+1440+280

Answer: There are 30 cubes in each layer and 3 layers. (Up to down.)

Explanation: You can multiply the x and y axis for one layer, and then count how many layers there are. There are 90 cubes in all.

I hope this helps, have a good day!

There would be a 1/36 chance of rolling a 6 then a 3 consecutively on a 6-sided die

Because the chance of rolling each of the numbers individually would be 1/6, and you are trying to roll 2 specific numbers in a row on a single die, you can simply multiply 1/6 by 1/6 to get your answer.

To calculate seed number, divide the total number of inches available for crop by the in-row crop spacing. For example, 120 inches divided by one inch per pea seed equals 120 pea seeds.

In botany, a seed is an undeveloped plant embryo and food reserve encased in a protective outer covering. In a broader sense, "seed" refers to anything that can be sown, such as seed and husk or tuber.

Seeds are formed when a ripened ovule is fertilised by pollen-derived sperm, resulting in a zygote. The embryo develops from the zygote within a seed, forming a seed coat around the ovule and growing to a certain size within the mother plant before growth stops.

The formation of seeds is a stage in the reproduction of seed plants (spermatophytes). Other plants, such as ferns, mosses, and liverworts, lack seeds and must reproduce exclusively through water.

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Proportion is the ratio of the two equal fractions. It compares the part of a whole to another part of another whole. Option c is the correct option which is, The test provides convincing evidence the proportion is greater than 90% but the actual proportion is equal to the 90%.

What is proportion?

proportion is the ratio of the two equal fraction. It compare the part of a whole to other part of of the another whole.

Given

Options for the following question are,

A) The test does not provide convincing evidence that the proportion is greater then 90 percent but the actual proportion is greater then 90 percent.

B) The test does not provide convincing evidence  the proportion is greater than 90% but the actual proportion is equal to the 90%.

C)The test provides convincing evidence the the proportion is greater than 90% but the actual proportion is equal to the 90%.

D)The test provides convincing evidence that the proportion is greater then 90 percent but the actual proportion is greater then 90 percent.

E) All type 1 error is not possible for this hypothesis test.

The Null Hypothesis for the given question is,

The proportion of all washers produced with the specified diameter is equal to 90 percent. The Null Hypothesis for the given case is true and actual proportion is equal to 90 percent.

Hence, option c is the correct option which is, The test provides convincing evidence tha the proportion is greater than 90% but the actual proportion is equal to the 90%.

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The number of grams of sugar that would be in a 200 ml glass of juice, given the carton, is 13. 2 grams of sugar

In a 250 ml glass of juice, we would see 16. 5 g of sugar. Given this information, we can find the amount of sugar in a 200 ml of juice by using direct proportion.

The amount of sugar in 200 ml of juice is :

= ( Amount of sugar in 250 ml x Quantity of juice ) / Quantity of base quantity of juice

= ( 16. 5 x 200 ) / 250

= 3, 300 / 250

= 13. 2 grams of sugar

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We can solve this equation using the distributive property. First, we will use the distributive property to multiply the 3y by 2.

The distributive property is a mathematical rule that allows you to multiply a single number by a group of numbers by multiplying the single number by each number in the group individually. This rule can be expressed in two ways. The first way is a(b + c) = ab + ac. The second way is a(b - c) = ab - ac.

This will give us 2x * 3y = 2(3y). Then, we will subtract 6 from both sides of the equation, which gives us 2x * 3y - 6 = 2(3y) - 6. We can then divide both sides of the equation by 6, which gives us 2x * 3y / 6 = 2(3y) / 6. Finally, we can divide both sides of the equation by 3y, which gives us 2x = -2. Therefore, the solution to 2x 3y = -6 is 2x = -2.

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No two values of x in the computation we just did are equal, there are 4 different values of x for which the sequence contains the value 2001.

An ordered list of numbers is all that a sequence is. Number series are collections of numbers that adhere to a pattern or guideline. An arithmetic sequence is one where the rule is to add or take away a number each time.

To estimate a few terms of the sequence in order to obtain a feel how it looks like.

In our case, the definition is that [tex]$\forall$[/tex] (for all) [tex]$n > 1: a_n=a_{n-1} a_{n+1}-1$[/tex].

This can be rewritten as [tex]$a_{n+1}=\frac{a_n+1}{a_{n-1}}$[/tex].

We have [tex]$a_1=x$[/tex] and [tex]$a_2=2000$[/tex], and we estimate:

[tex]$& a_3=\frac{a_2+1}{a_1}=\frac{2001}{x} \\[/tex]

[tex]$& a_4=\frac{a_3+1}{a_2}=\frac{\frac{2001}{x}+1}{2000}=\frac{2001+x}{2000 x} \\[/tex]

[tex]$& a_5=\frac{a_4+1}{a_3}=\frac{\frac{2001+x}{2000 x}+1}{\frac{2001}{x}}=\frac{\frac{2001+2001 x}{2000 x}}{\frac{2001}{x}}=\frac{1+x}{2000} \\[/tex]

[tex]$& a_6=\frac{a_5+1}{a_4}=\frac{\frac{1+x}{2000}+1}{\frac{2001+x}{2000 x}}=\frac{\frac{2001+x}{2000}}{\frac{2001+x}{2000 x}}=x \\[/tex]

[tex]$& a_7=\frac{a_6+1}{a_5}=\frac{x+1}{\frac{1+x}{2000}}=2000[/tex]

At this point we see that the sequence will become periodic: we contain [tex]$a_6=a_1, a_7=a_2$[/tex], and each subsequent term exists uniquely determined by the previous two.

Hence 2001 appears, it contains to be one of [tex]$a_1$[/tex] to [tex]$a_5$[/tex].

As [tex]$a_2=2000$[/tex], we only have four possibilities left.

Clearly [tex]$a_1=2001$[/tex] for x = 2001, and [tex]$a_3=2001$[/tex] for x = 1.

The equation [tex]$a_4=2001$[/tex]

solves to [tex]$x=\frac{2001}{2000 \cdot 2001-1}$[/tex], and the equation [tex]$a_5=2001$[/tex] to [tex]$x=2000 \cdot 2001-1$[/tex]

There are four alternative values of x for which the sequence contains the value 2001 since no two values of x are equal in the computation we just performed.

Therefore, the correct answer is option (D) 4.

The complete question is:
Consider sequences of positive real numbers of the form x, 2000, y, ........  in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x does the term 2001 appear somewhere in the sequence?

(A) 1

(B) 2

(C) 3

(D) 4

(E) more than 4

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Answer:

[tex] \sqrt{a {}^{2} + b {}^{2} }[/tex]

AE is congruent to CE.We can prove by assuming two triangle in the given diagram and by using SAS rule.

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle then the two triangles are said to be congruent by SSS rule. In the above-given figure, AB= PQ, BC = QR and AC=PR, hence Δ ABC ≅ Δ PQR.

Alternate angles are angles that occur on opposite sides of the transversal line. If two parallel lines are cut by a transversal then the alternate angles are equal.The pair of angles formed on the inner side of the parallel lines but on the opposite sides of the transversal are called alternate interior angles.

Now we have

Given a triangle ABC.Where E is the midpoint of AC. We have to prove that AE is congruent to CE.

In ΔAED and ΔCED

ED=ED              (∵Common side are equal)

∠AED=∠CED       (∵Alternate angles)

∠A=∠C        (∵Alternate angles)

By ASA rule, ΔAED≅ΔCED

By Corresponding Parts of Congruent triangles

AE=EC

Hence, AE is conruent to CE.

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The diameter of the circle is 30 feet

To compute the diameter of the circle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the diameter of the circle, and the other two sides are the radius and the distance between the chord and the center of the circle.

So, we can write the equation:

diameter^2 = radius^2 + (distance between chord and center)^2

We know the radius is half the diameter, so we can substitute that in:

diameter^2 = (diameter/2)^2 + (15)^2

And we can solve for the diameter:

diameter^2 = diameter^2/4 + 225

diameter^2 = diameter^2/4 + 225

4diameter^2 = diameter^2 + 900

3diameter^2 = 900

diameter^2 = 900/3

diameter = sqrt(900/3)

So the diameter of the circle is 30 feet.

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In two-dimensional space, only two coordinates are required to specify the location and orientation of a rigid body.

In two-dimensional space, a rigid body can only move in two directions (up/down and left/right) and rotate around a single axis. As a result, only two coordinates are needed to specify the location and orientation of a rigid body in two-dimensional space. The two coordinates needed to specify the rigid body's position are the x-coordinate and y-coordinate, which define the position of the body in the plane. The orientation of the rigid body can be determined by determining the angle between the x-axis and the body's orientation, which is referred to as the angle of rotation. The combination of these two coordinates (position and rotation) specify the full state of the rigid body in two-dimensional space.

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Answer:

When plotting points on the coordinate plane below, which point would lie on both the x-axis and the y-axis? the answer is its the origin  (0, 0)

Step-by-step explanation:

The answer as an exact decimal = -0.84 and simplified fraction = −21/25.

Simplifying a fraction is the process of reducing a fraction to its most basic form. If the numerator and denominator of a fraction have no common factors other than one, the fraction is in its simplest form.

When solving fraction problems, we must first simplify them. Even if we simplify them, the fraction's value will remain unchanged. This means that the simplified and actual fractions are equivalent fractions.

Given that

-67/50 + 1.5 − 100% = ?

Lets solve

= -67/50 + 1.5 − 100%

= -67/50 + 1.5 − (100 × 0.01)

= -67/50 + 3/2 - 1

= -67/50 + 75/50 - 50/50

= (-67 + 75- 50)/50

= −42/50

= −21/25

= -0.84

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Answer:

slope = 2

y-int = -3

Step-by-step explanation:

y  =  2 x  −  3 is the slope-intercept form equation

Answer:

Slope: -2

Y intercept: (0,3)

Answer:

The US Consumer Price Index (CPI) increased 8.3% in the 12 months through August, with rent, food and healthcare accounting for the rise Excluding volatile food and gas prices, inflation climbed 6.3% year-on-year in July and 8.2% in September. US inflation ticked back up in August despite plunging gas prices.

citations: https://nypost.com/2022/10/13/inflation-hits-8-2-in-september-as-core-prices-surge/Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

g(-1) = 3(-1)² - 2(-1) + 7 / 2(-1) + 5

= 3-(-2)+7 / -2+5

= 5+7/-3

= 12/-3

= -4

Answer:

140 bois

Step-by-step explanation:

Observe que:

1 hectare = 10000m²

Na Fazenda Santa Elisa, principal atividade da pecuária, cada hectare deve ser ocupado por 20 bois

Isso significa:

10000m² = 20 bois

O número de bois que podem ser criados no local de 70000 m² é calculado como:

10000m² = 20 bois

70000m² = x

Multiplicação cruzada

10000m² × x = 70000m² × 20 bois

x = 70000m² × 20 bois / 10000m²

x = 140 bois

Portanto, 140 bois podem ser criados em um terreno com 70000m².

Answer:

C. the function f(x) has the greater y-intercept by 72 units

Step-by-step explanation:

find f(x) y-intercept:

[tex]3(0-5)^2\\\\=3(-5)^2\\\\=3(25)\\\\=75[/tex]

the y-intercept of g(x) is 3

to find the difference subtract 3 from 75 and you get 72