Answer:
x=14
PQ=46
Step-by-step explanation:
PT and TQ are equal, so we can set up the equation like this: PT=TQ
23=2x-5
calculate to find x
x=14
PQ is just PT+TQ so 23+23=46
Answer:
9. a = -7
10. x = 1
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
a + 6a - 14 = 3a + 6a
<u>Step 2: Solve for </u><em><u>a</u></em>
- Combine like terms: 7a - 14 = 9a
- Subtract 7a on both sides: -14 = 2a
- Divide 2 on both sides: -7 = a
- Rewrite: a = -7
<u>Step 3: Check</u>
<em>Plug in a into the original equation to verify it's a solution.</em>
- Substitute in <em>a</em>: -7 + 6(-7) - 14 = 3(-7) + 6(-7)
- Multiply: -7 - 42 - 14 = -21 - 42
- Subtract: -49 - 14 = -63
- Subtract: -63 = -63
Here we see that -63 is equal to -63.
∴ a = -7 is a solution of the equation.
<u>Step 4: Define equation</u>
-12 - 4x = 8x + 4(1 - 7x)
<u>Step 5: Solve for </u><em><u>x</u></em>
- Distribute 4: -12 - 4x = 8x + 4 - 28x
- Combine like terms: -12 - 4x = -20x + 4
- Add 20x on both sides: -12 + 16x = 4
- Add 12 on both sides: 16x = 16
- Divide 16 on both sides: x = 1
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: -12 - 4(1) = 8(1) + 4(1 - 7(1))
- Multiply: -12 - 4 = 8 + 4(1 - 7)
- Subtract: -16 = 8 + 4(-6)
- Multiply: -16 = 8 - 24
- Subtract: -16 = -16
Here we see that -16 does indeed equal -16.
∴ x = 1 is a solution of the equation.
So, we know the center is at -3,-1, ok
hmmm what's the radius anyway? well, we know that there's a point at 1,2 that is on the circle's path...hmmmm what's the distance from the center to that point? well, is the radius, let's check then.
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ -1}})\quad % (c,d) &({{ 1}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ r=\sqrt{[1-(-3)]^2+[2-(-1)]^2}\implies r=\sqrt{(1+3)^2+(2+1)^2} \\\\\\ r=\sqrt{16+9}\implies r=\sqrt{25}\implies r=5](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%28%7B%7B%20-3%7D%7D%5Cquad%20%2C%26%7B%7B%20-1%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0A%26%28%7B%7B%201%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ar%3D%5Csqrt%7B%5B1-%28-3%29%5D%5E2%2B%5B2-%28-1%29%5D%5E2%7D%5Cimplies%20r%3D%5Csqrt%7B%281%2B3%29%5E2%2B%282%2B1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ar%3D%5Csqrt%7B16%2B9%7D%5Cimplies%20r%3D%5Csqrt%7B25%7D%5Cimplies%20r%3D5)
so, what's the equation of a circle with center at -3, -1 and a radius of 5?
Answer:
The answer is B.(5,10)
Step-by-step explanation:
1. y = 2(5)
y = 10
2.y = -2(5)+20
y = -10+20
y = 10
Answer: 40
Step-by-step explanation:
Number of correct questions Sally got = 28 questions
Percentage of correct questions answered= 70% on the exam,
Total number of questions in the exam = Unknown
Let the total questions in the exam be represented as y.
Since Sally got 70% correctly, this will be:
70% of y = 28
70/100 × y = 28
0.7 × y = 28
0.7y = 28
Divide both side by 0.7
0.7y/0.7 = 28/0.7
y = 40
There are 40 questions in the exam.