Answer:
Matt has 7 cards.
Step-by-step explanation:
Let K, M and Z represent number of cards that Kate, Matt and Zach have.
We have been given that together Kate and Matt have 47 cards. We can represent his information in an equation as:

We are also told that Kate and Zach combine cards they have 126. We can represent his information in an equation as:

Further, Matt and Zach combine they have 93. We can represent his information in an equation as:

Upon subtracting equation (3) from equation (2), we will get:



Upon substituting this value in equation (1), we will get:




Therefore, Matt has 7 cards.
Answer:
21 dollars
Step-by-step explanation:
Answer:
<em>Annie will be able to borrow</em><em> $ 7,716.00 </em>for the playground using her car a collateral (option b).
Explanation:
Interpretation of the problem:<em> to take out a loan to put a new playground in her yard for her kids, Annie offers her car which is worth $ 7,800 as collateral.</em> Since <em>the loan officer at the bank is permitted to loan Annie 92% of the value of her collateral</em>, in order to know <em>how much Annie will be able to borrow</em>, you must use<em> </em>percentage calculations.
Percent is a definition: percent is the ratio of an amount with respect to one hundreed. The mathematical expressions derived from that definition is:
- Percent, % = (amount / base) × 100
In this case, the percent that <em>the officer is permitted to loan</em> is known, <em>92%</em>, the amount to <em>borrow</em> is unknown (x), and the base is the <em>value of her car </em>(<em>the collateral</em>), <em>$ 7,800</em>, which leads to the following equation:
Now, you can solve for x:
- x = 7,800 × 92/100 = 7,800 × 0.92 = 7,176.00
In conclusion, <em>Annie will be able to borrow $ 7,716.00 for the playground using her car as collateral</em>.
The answer of
<span>-45+(-30)-90= -165
Hope this helps <3
</span>
Answer:
Depth of the submarine = 668.09 feet
Step-by-step explanation:
From the figure attached,
In triangle ABC,
Distance between a navy cruiser and a nuclear submarine = 2500 feet
Angle between the water level and the submarine = 15.5°
By applying sine rule in the given triangle,
sin(∠BAC)° = 
sin(15.5°) = 
BC = 2500[sin(15.5)]
BC = 668.09 feet
Therefore, submarine is 668.09 feet deep in the sea.