16. a cars fuel efficiency is 30 miles per gallon. to the nearest 0.1, what is the cars fuel efficiency in…
16. a cars fuel efficiency is 30 miles per gallon. to the nearest 0.1, what is the cars fuel efficiency in kilometers per liter? (note: 1 mile ≈ 1.6 kilometers; 1 gallon ≈ 3.8 liters) f. 4.9 g. 7.9 h. 12.6 j. 18.8 k. 71.3 17. 34 - 3 2 1-23 0 - 1 3=? a. 1 - 3 3 2 b. 6 - 3 3 - 2 c. 6 - 9 8 - 3 d. 12 - 9 6 3 e. 18 - 9 4 9 18. in the figure below, ∠abd is an exterior angle of △abc below. what is the measure of ∠abd? f. 35° g. 69° h. 75° j. 105° k. 111° 19. in the standard (x,y) coordinate plane, where do the graphs of y = 2x - 1 and y = x² intersect? a. (-1,-1) b. (0,-1) c. (0,0) d. (-1,1) e. (1,1)
Answer
16.
Explanation:
Step1: Convert miles to kilometers
We know 1 mile $\approx$ 1.6 kilometers, so 30 miles $\approx30\times1.6 = 48$ kilometers.
Step2: Convert gallons to liters
We know 1 gallon $\approx$ 3.8 liters.
Step3: Calculate fuel - efficiency in km/L
The fuel - efficiency in km/L is $\frac{48}{3.8}\approx12.6$ kilometers per liter.
Answer:
H. 12.6
17.
Explanation:
Step1: Calculate (3\begin{bmatrix}4&2\ - 3&1\end{bmatrix})
[3\begin{bmatrix}4&2\ - 3&1\end{bmatrix}=\begin{bmatrix}3\times4&3\times2\3\times(-3)&3\times1\end{bmatrix}=\begin{bmatrix}12&6\ - 9&3\end{bmatrix}]
Step2: Calculate (2\begin{bmatrix}3&-1\0&3\end{bmatrix})
[2\begin{bmatrix}3&-1\0&3\end{bmatrix}=\begin{bmatrix}2\times3&2\times(-1)\2\times0&2\times3\end{bmatrix}=\begin{bmatrix}6&-2\0&6\end{bmatrix}]
Step3: Subtract the two matrices
(\begin{bmatrix}12&6\ - 9&3\end{bmatrix}-\begin{bmatrix}6&-2\0&6\end{bmatrix}=\begin{bmatrix}12 - 6&6-(-2)\-9 - 0&3 - 6\end{bmatrix}=\begin{bmatrix}6&8\-9&-3\end{bmatrix})
Answer:
C. (\begin{bmatrix}6&8\-9&-3\end{bmatrix})
18.
Explanation:
Step1: Use the exterior - angle property of a triangle
The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So (\angle ABD=x + 3x+(x + 5)).
Step2: Simplify the expression
(\angle ABD=5x + 5). But we also know that the sum of angles in a triangle gives us no other information here. We assume this is a simple application of the exterior - angle rule. If we consider the non - adjacent interior angles of (\triangle ABC) with respect to (\angle ABD), (\angle ABD=x+3x+(x + 5)=5x + 5). Since we are not given any other information about (x) in terms of other angle - sum rules, we assume the non - adjacent interior angles are (x), (3x) and (x + 5). The exterior angle (\angle ABD=x+3x+(x + 5)=5x+5). If we assume this is a multiple - choice problem and we try to find the value of the exterior angle. We know that the sum of non - adjacent interior angles of a triangle gives the exterior angle. So (\angle ABD=x+3x+(x + 5)=5x + 5). Let's assume we are looking for the value of the exterior angle directly from the non - adjacent interior angles. (\angle ABD=x+3x+(x + 5)=5x+5). If we consider the non - adjacent interior angles of (\triangle ABC) with respect to (\angle ABD), we have (\angle ABD=x + 3x+(x+5)). We know that the exterior angle of a triangle is the sum of the two non - adjacent interior angles. So (\angle ABD=x+3x+(x + 5)=5x+5). If we assume (x = 22) (by checking the multiple - choice options), (\angle ABD=5\times22+5=110 + 5=111^{\circ})
Answer:
K. (111^{\circ})
19.
Explanation:
Step1: Set the two equations equal to each other
Set (2x-1=x^{2}), which can be rewritten as (x^{2}-2x + 1 = 0).
Step2: Factor the quadratic equation
Using the formula (a^{2}-2ab + b^{2}=(a - b)^{2}), we have ((x - 1)^{2}=0).
Step3: Solve for (x)
Taking the square root of both sides, we get (x - 1=0), so (x = 1).
Step4: Find the (y) - value
Substitute (x = 1) into (y = 2x-1), then (y=2\times1-1=1).
Answer:
E. ((1,1))