Which equation has solution x = -3?
A) 2x - 7 = -1
B) 3x + 8 = 1
C)
1
2
x + 8 = 10
D)
1
2
(2x - 6) = -6

The graph of [tex]y=4x+3[/tex] is a line with a slope of 4, meaning for every unit moved to the right on the x-axis, you move up four units on the y-axis. The y-intercept is 3, so the line intersects the y-axis at the point (0,3). We plot these points and draw the line through them for the complete graph.

The question asks, which of the following shows the graph of [tex]y = 4x + 3?[/tex]This is a linear equation in the format of y=mx+b, where 'm' is the slope of the line and 'b' is the y-intercept. In this case, 'm' is 4, so for every step you move to the right on the x-axis, you move four steps up on the y-axis. 'b' is 3, so the line intersects the y-axis at the point (0,3). To graph this equation, start at the point (0,3) and for every 1 unit you move to the right, move up by 4 units. Repeat this process with other values of x to find corresponding values of y. Points are then plotted on the graph and a line is drawn through them showing the relationship between x and y.

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Final answer:

The truth value of the conditional statement 'If the snow is white, then the grass is red' cannot be determined to be true or false without context, as it is a statement that requires evaluation of its antecedent and consequent. In logic, a conditional statement is true unless the antecedent is true and the consequent is false.

Explanation:

The truth value for the conditional statement "If the snow is white, then the grass is red," cannot be evaluated as true or false based solely on the content of the statement. In logic, a conditional statement is considered to be true unless a situation occurs where the first part (the antecedent) is true and the second part (the consequent) is false.

Here, the statement "the snow is white" is true, but the statement "the grass is red" can be false, as grass is typically green. This illustrates an important logical principle where the truthfulness of a conditional does not require that the consequent actually follows from the antecedent. To evaluate the truth of a conditional statement, it would be more appropriate to look for a counterexample that disproves it or involves a scenario where the antecedent is true and the consequent is false.

Answer:

[tex]w_{uu} = 72u^{7}[/tex]

[tex]w_{uv} = w_{vu} = 0[/tex]

[tex]w_{vv} = 42v^{5}[/tex]

Step-by-step explanation:

We can have the second partial derivatives of w in relation to u, v and uv. So

[tex]w = u^{9} + v^{7}[/tex]

[tex]w_{u} = 9u^{8}[/tex]

[tex]w_{uu} = 72u^{7}[/tex]

[tex]w_{uv} = w_{vu} = 0[/tex]

[tex]w_{v} = 7v^{6}[/tex]

[tex]w_{vv} = 42v^{5}[/tex]

Final answer:

The second partial derivatives of w = u^9 + v^7 are w_uu = 72u^7, w_uv = 0, and w_vv = 42v^5.

Explanation:

To find all the second partial derivatives of w = u^9 + v^7, we need to differentiate twice with respect to each variable. Let's start:

First, find the first partial derivatives:
wu = 9u^8 (differentiating with respect to u)
wv = 7v^6 (differentiating with respect to v)

Now, take the second partial derivatives:
wuu = 72u^7 (differentiating wu with respect to u)
wuv = 0 (differentiating wu with respect to v)
wvv = 42v^5 (differentiating wv with respect to v)

So, the second partial derivatives of w = u^9 + v^7 are wuu = 72u^7, wuv = 0, and wvv = 42v^5.

The answer should be

228

The solution to the mathematical inequality equation 0.35x - 4.8 < 5.2 - 0.9x is the interval x < 8.

In order to find the solution to the equation 0.35x - 4.8 < 5.2 - 0.9x, you first need to rearrange the terms in the equation such that all terms involving x are on one side of the inequality and the other terms are on the other side. Starting with: 0.35x - 4.8 < 5.2 - 0.9x, if we add 0.9x to both sides we get 0.35x + 0.9x < 5.2 - 4.8, which simplifies to 1.25x < 10.

Next, to isolate 'x' we divide through by 1.25, which gives us: x < 10/1.25 which simplifies to x < 8. Therefore the answer to the equation 0.35x - 4.8 < 5.2 - 0.9x is the interval x < 8.

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Answer: B

Step-by-step explanation:

plato

The number is 21.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

5/7 of M = 15

This can be written as,

(5/7)M = 15

M = 15 x 7/5

M = 3 x 7

M = 21

Thus,

The number is 21.

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Answer: C. 19.5 in × 29.25 in

Step-by-step explanation: (50 x .39) x (75 x .39)

The radius of a globe is 7.5 inches. What is the volume of the globe? Use 3.14 for pi.

Volume of the globe=[tex] \frac{4}{3} \pi r^{3} [/tex]

Volume of the globe=[tex] \frac{4}{3}*3.14*7.5^{3} [/tex]

Volume=[tex] \frac{4}{3}*3.14*421.875 [/tex]

Volume=[tex] \frac{4}{3}*1324.6875 [/tex]

Volume=[tex] \frac{5928.75}{3} [/tex]

Volume=1766.25[tex] inches^{3} [/tex]

Volume of Globe=1766.25[tex] in^{3} [/tex]

Answer: 1766.25

Step-by-step explanation: tryust

Here we are given two types of data : Time and Temperature.

We can plot one of these on x axis and the other on y axis.

So we can use a line graph here.

Melvin and each of his 2 friends get [tex]\( \frac{1}{6} \)[/tex] of the cake each.

Sure! If Melvin has [tex]\( \frac{1}{2} \)[/tex] of a cake and he wants to share it equally with each of his 2 friends and himself, we need to find out how much each person gets.

First, we need to find out how many people are sharing the cake. Melvin himself plus his 2 friends make a total of 3 people.

Now, to divide [tex]\( \frac{1}{2} \)[/tex] of the cake equally among 3 people, we divide [tex]\( \frac{1}{2} \)[/tex] by 3:

[tex]\[ \frac{1/2}{3} = \frac{1}{2} \times \frac{1}{3} \][/tex]

To multiply fractions, we multiply the numerators together and the denominators together:

[tex]\[ = \frac{1 \times 1}{2 \times 3} \][/tex]

[tex]\[ = \frac{1}{6} \][/tex]

So, each person gets [tex]\( \frac{1}{6} \)[/tex] of the cake.

Therefore, Melvin and each of his 2 friends get [tex]\( \frac{1}{6} \)[/tex] of the cake each.

Answer:

Answer:

Part A) The quantities are [tex]30\ piece\ of\ sushi[/tex] and [tex]20\ bagels[/tex]

Part B) [tex]\$80[/tex]

Part C) The income effect is a loss of [tex]\$20[/tex]

Step-by-step explanation:

Part A)

Let

x-----> the number of piece of sushi

y----> the original number of bagels

we know that

[tex]2x=60[/tex] ------> [tex]x=30\ piece\ of\ sushi[/tex]

[tex]2y=40[/tex] ------> [tex]y=20\ bagels[/tex]

Part B) At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)?

Bagels

[tex]20(1)=\$20[/tex]

Sushi

[tex]30(2)=\$60[/tex] -----> is the same

The total cost is

[tex]\$20+\$60=\$80[/tex]

so

The same quantities would have cost [tex]\$80[/tex]

Part C) Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels?

Find the difference

[tex]\$100-\$80=\$20[/tex]

therefore

The income effect is a loss of [tex]\$20[/tex]

At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.

We have,

The equation θ(t) = a + bt² - ct³ represents the angular position of a point on the amusement park ride as a function of time.

Given:

a = 0.3 rad

b = 0.85 rad/s²

c = 0.035 rad/s³

In this equation,

θ(t) represents the angular position of the point on the ride at time t.

The term a is the initial angular position when t = 0, which is 0.3 radians.

The term bt² represents the angular displacement due to the linearly increasing angular velocity.

The coefficient b determines the rate of change of the angular displacement over time.

The term -ct³ represents the angular displacement due to the cubic decrease in angular acceleration.

To find the angular position at a specific time t, substitute the given values of a, b, c, and the desired value of t into the equation

θ(t) = a + bt² - ct³.

For example, if we want to find the angular position at t = 2 seconds:

θ(2) = 0.3 + 0.85 * (2²) - 0.035 * (2³)

= 0.3 + 0.85 * 4 - 0.035 * 8

= 0.3 + 3.4 - 0.28

= 3.42 radians

Therefore,

At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.

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The angular position of a point on a ride is given by the equation θ(t) = a + bt² - ct³. Factors such as the moment of inertia can change the angular acceleration in the system. When a child is on the merry-go-round, the moment of inertia increases, leading to a decrease in angular acceleration.

The angular position of a point on an amusement park ride can be described by the equation θ(t) = a + bt² - ct³. In this equation, angular position is represented by θ(t), 'a' represents the initial angular position (0.3 rad), 'b' represents the angular velocity (increase in angular position per unit time - 0.85 rad/s2) and 'c' is the rate of change in angular velocity or the angular acceleration (0.035 rad/s3).

The angular acceleration can change due to factors such as a change in the moment of inertia. For example, when a child is on a merry-go-round, the combined moment of inertia is greater, therefore reducing the angular acceleration. The moment of inertia depends on factors such as the mass and the location of that mass relative to the axis of rotation. The child can be approximated as a point mass at a distance of 1.25 m from the axis of rotation.

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