Answer:
2 ≤ x < 7
Step-by-step explanation:
-1 ≤ x – 3 < 4
Add 3 to each side
-1+3 ≤ x – 3+3 < 4+3
2 ≤ x < 7
Answer:
Husband:
The husband will have 16.35 mg of caffeine in his body at 7 pm.
Woman:
The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.
Step-by-step explanation:
The amount of caffeine in the body can be modeled by the following equation:
In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.
110 mg of caffeine at 8 am,
So 
Husband
Half life of 4 hours. So
Applying ln to both sides
So for the husband
At 7 pm
7 pm is 11 hours after 8 am, so this is C(11)
The husband will have 16.35 mg of caffeine in his body at 7 pm.
Pregnant woman
Half life of 10 hours. So
Applying ln to both sides
At 7 pm
7 pm is 11 hours after 8 am, so this is C(11)
The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.
Answer:
Image A shows a reflection.
area of rectangle = length x width
this is the formula to find it.
now , put the values of length and width,
=> area= 12 x 3 x 6 x 2
=> area = 432 feet^2
Hope this helps!
Here’s the proof:
The triangle is an Isosceles Triangle. An Isosceles Triangle is a type of triangle that has 2 congruent sides. There is a Theorem called The Isosceles Triangle Theorem, in which states that if a triangle has 2 congruent sides, then it is an Isosceles Triangle, and the angles oppositely the congruent sides will be congruent. Therefore, we know that the triangle is Isosceles because it has 2 congruent sides, so the angles opposite those sides are congruent. We first need to find the angle measures.
1.) Finding the angle measures using the Triangle Sum Theorem. The Triangle Sum Theorem states that all 3 angles in a triangle must sum up to 180°. So, we can create an Algebraic equation to solve and figure out what the angle measures are of the two angles at the bottom of the triangle because they are opposite to the congruent sides.
Equation:
26+2x=180. We know that one angle measure is 26°, and we know the other 2 are angles are congruent, so we will call them X, and there are two of them, so we call them 2x.
26-26+2x=180-26
2x=154
2x/2=154/2
x=77.
Therefore, the angles measure 77°. To check that we can just plug them back into our equation:
26+2(77)=180.
180=180.
The angle measures are correct.
2.) Since we know the angle measures of the triangle, we can use the Alternate Exterior Angles Theorem, which states: if a transversal is intersected by two parallel lines, then the alternating exterior angles are congruent. We can see in the picture that the lane with the triangle on top and trapezoid at the bottom is a transversal (transversal=line intersected by two parallel lines). We can also see that the two lines with arrows are parallel because they are marked parallel with arrows. Therefore, we have a transversal intersected by two parallel lines, so the angles outside the parallel lines and and opposite each other are congruent.
We know that the two angles at the base of the triangle are 77°. The left base angle in the triangle is outside the parallel lines, so angle n or n° must also be 77° because they are both outside the parallel lines (exterior) and alternating from each other.
Therefore, n°=77°
