Answer:
Number of guests = 13
Sauce = 52 ounces
Dough = 78 ounces
Step-by-step explanation:
you are having a pizza making party. You will need 6 ounces of dough and 4 ounces of sauce for each person at the party (including myself the host) Once you have a total count of guests you have exactly the amount needed for ingredients. the dough and sauce that I have is 130 ounces all together. How many ounces of dough did I buy? Explain How many ounces of sauce did I buy? Explain How many guests are coming to the party? Explain
Dough = 6 ounces
Suase = 4 ounces
Dough + sauce = 6 + 4 = 10
Let x = total number of guests
Dough ingredients + sauce ingredients = 130
10x = 130
Divide both sides by 10
x = 130/10
= 13
x = 13
Number of guests = 13
Total ounces of dough = 6 ounces × 13 guests
= 78 ounces of dough
Total ounces of sauce = 4 ounces × 13 guests
= 52 ounces of sauce
Therefore,
Number of guests = 13
Sauce = 52 ounces
Dough = 78 ounces
You can use the Pythagorean Theorem to find the length of the third side AB (Identified as "x" in the figure attached in the problem), which says that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:
a² = b²+c²
As we can see the figure, the triangle does not have an angle of 90°, but it can be divided into two equal parts, leaving two triangles with a right angle. We already have the values of the hypotenuse and a leg in triangle "A" , so we can find the value of the other leg:
b = √(a²-c²) b = √(10²-4²) b = 9.16
With these values, we can find the hypotenuse in the triangle "B": x = √b²+c² x = √(9.16)²+(4)² x = 10
Let the walker’s speed be W, then the biker’s is W+1.5W=2.5W. Difference in speed is 1.5W. Distance=speed times time, so 12.5=1.5W×1.5=2.25W, and W=12.5/2.25=1250/225=50/9=5.56 mph. The biker’s speed is 2.5W=125/9=13.89 mph to 2 Dec places.
(Note: “1.5 times faster than a walker’s speed” could not reasonably mean the biker’s speed=1.5W because this would give W=16.67 mph, which is very fast for a runner, let alone a walker (!), and a biker’s speed of 25mph.)
Answer:
Your answer would be 37°
Step-by-step explanation:
Since BC and DE are parallel, certain angles will be the same, such as the missing interior angle of the triangle and ∠DAF, which will also have the same measure as x.
We know that the sum of all of the interior angles of a triangle must equal 180°. So, we add 41 and 102 to get 143. This means that the missing interior angle must be 37°, since 37+143=180.
As mentioned above, because BC and DE are parallel, the missing interior angle has the same measure as ∠DAF, which is a vertical angle to x, and therefore also has the same measure. So, the measure of x is 37°.
Hope this helps you!