Peter plays a game where each correct answer gets him -3 points and every incorrect answer gets him 1 point. If he got 6 correct and 4 incorrect answers, how many points does he have? Write an equation and solve.

The antilog provides the solution to the logarithmic equation. Then x has values of 2 and 4.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The logarithmic equation is given below.

[tex]\log _6(x^{2} +8)= 1+ \log _6x\\\\\log _6(x^{2} +8)= \log_66+ \log _6x\\\\\log _6(x^{2} +8)= \log _66x\\[/tex]

Take antilog, then we have

[tex]\begin{aligned} x^{2} +8 &= 6x\\\\x^2 -6x + 8 &= 0\\\\x^2 -4x - 2x +8 &=0\\\\(x-4)(x-2) &= 0\\\\x&= 2, 4\end{aligned}[/tex]

Then the value of the x is 2 and 4.

More about the factorization link is given below.

https://brainly.com/question/6810544

Answer:

D. 6(x+2y)-y

Step-by-step explanation:

Both expressions can be simplified into 6x + 11y

3(2x+4y)-y
6x + 12y - y
6x + 11y

6(x+2y)-y
6x + 12y - y
6x + 11y

Answer:

D. 6(x+2y)-y

Step-by-step explanation:

To solve for the equivilent expression, begin by simplifying the given expression. (1) To simplify 3(2x+4y)-y, you can first multiply 3 into the parentheses then combine like terms; (6x+12y)-y or 6x + 12y - y --> 6x + 11y. (2) Solve to find which expression listed will yield the same product, 6x + 11y, when simplified as well. This is quiet straightfoward to see and you wont be needing to solve each individual problem. 6(x+2y)-y will simplify to 6x + 12y - y which is then equal to --> 6x + 11y. Meaning, D. 6(x+2y)-y is equvillent to 3(2x+4y)-y.

Answer:

Area of Trapezium=1/2h(L1+L2)

I think it will help you

Answer:

Problem 4: Dog pens 2 and 3

Problem 5: Dog Pens 1 and 2

Problem 6: 6cm and 6cm

problem 7: A

Step-by-step explanation:

The estimated difference of the area of Colorado and Wyoming in scienfic notation is  2 x [tex]10^{-1}[/tex]m².

Scienfic notation is used in expressing large numbers in smaller numbers. In order to write a number in stscienfic notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

Area of Colorado = (6.12 x [tex]10^{5}[/tex]) x (4.5 x [tex]10^{5}[/tex]) = 27.54 x [tex]10^{10}[/tex]

= 2.8 x [tex]10^{11}[/tex]m²

Difference in the areas = 2.8 x [tex]10^{11}[/tex]m² - 2.6 x x [tex]10^{11}[/tex]m² = 0.2m²

= 2 x [tex]10^{-1}[/tex]m²

To learn more about scienfic notation, please check: https://brainly.com/question/25334755

Answer:

B

Step-by-step explanation:

Inverse is opposite. So, domain becomes range and range becomes domain

x<2 of domain becomes y<2 for range

y>0 of range becomes x>0 of domain

Answer:

1. C 3 1/8

2. A 3

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

12 hotdogs per min × 8 minutes = 96

145-96= 49

So he will have 49 hotdogs left.

Answer: 1.8 X 10^8

Step-by-step explanation: 6.0 X 10^7 times .3 = 1.8 X 10^8

Answer:

39

Step-by-step explanation:

Let h: hit

Let n: not hit

1) We can create two equations and solve them simultaneously using the substitution method or elimination.

h + n = 100

12h - 4n = 224

2) Solve them. I will demonstrate using the substitution method.

n = 100 - h

-----------------------

12h - 4(100 - h) = 224

12h - 400 + 4h = 224

16h = 224 + 400

16h = 624

h = 624/16

h = 39

3) Substitute the result into one of the equations above.

n = 100 - 39

n = 61

Since the question wants you to write the number of times the dragon was hit, the answer is 39.

Answer:

The answer is C. 418cm2

Step-by-step explanation:

A rectangular prism with a volume of 400 cubic centimeters has dimensions of 5 cm, 8 cm, and 10 cm with the value of x being 4.

The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.

Volume of rectangular prism = (length x width x height)

A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeter, 2x centimeters, and x + 6 centimeters.

Volume of rectangular prism = (length x width x height)

      400 cm³  =( x + 1 )(2x)(x + 6 )

        400 cm³  =( x + 1 )(2x)(x + 6 )

Substitute 4cm as the value of x.

x + 1 centimeters = 4 cm + 1 cm = 5 cm

2x centimeters = 2 ( 4cm) = 8 cm

x + 6 centimeters = 4 cm + 6 cm = 10 cm

Volume of rectangular prism  = 10 cm × 5 cm × 8 cm

           = 400 cm³

Thus, the given rectangular prism of 400 cubic centimeters has dimensions of 5 cm, 8 cm, and 10 cm.

Learn more about rectangular prism;

https://brainly.com/question/15843335

Answer:

Step-by-step explanation:

its 10

Answer:

1/4

Step-by-step explanation:

Amplitude is equal the A part of the function which is 1/4.

Answer:

4

Step-by-step explanation:

360 degrees in a circle /12  numbers on clock= 30 degrees for each number 120/30=4

Answer:

Step-by-step explanation:

Equation

Let the angles measure = x

Let the complimentary angle = 90 - x

3x - (90 - x) = 46                      Remove the brackets

Solution

3x - 90 + x = 56                       Combine like terms on the left

4x - 90 = 56                             Add 90 to both sides

4x - 90 +90 = 56 + 90             Combine

4x = 146                                    Divide by 4

4x/4 = 146/4        

x = 36.5

Answer

The given angle is 36.5

The options have not been given but three correct alternatives have been presented as the solution.

We have given,

[tex]\frac{c^2-4}{c+3} /\frac{c+2}{3(c^2-9)}[/tex]

Applying the rule a^2-b^2 to the numerator of the first term and the denominator of the second term,

[tex](a^2-b^2)=(a-b)(a+b)[/tex]

By applying the above formula we have:

[tex]=\frac{c^2-2^2}{c+3} /\frac{c+2}{3((c+3)(c-3)}[/tex]

[tex]=\frac{(c-2)(c+2)}{c+3} /\frac{c+2}{3((c+3)(c-3)}[/tex]

Therefore the solution is,

[tex]=(c-2) \times 3(c-3)\\\\=3(c^2-5c+6)\\\\=3c^2-15c+18[/tex]

To learn more about the expression visit:

https://brainly.com/question/723406

Answer:

C.) StartFraction c squared minus 4 Over c + 3 EndFraction times StartFraction 3 (c squared minus 9) Over c + 2 EndFraction"/>

Step-by-step explanation:

Which expression is equivalent to StartFraction c squared minus 4 Over c + 3 EndFraction divided by StartFraction c + 2 Over 3 (c squared minus 9) EndFraction?

StartFraction c + 3 Over c squared minus 4 EndFraction times StartFraction c + 2 Over 3 (c squared minus 9) EndFraction

StartFraction c squared minus 4 Over c + 3 EndFraction divided by StartFraction 3 (c squared minus 9) Over c + 2 EndFraction

StartFraction c squared minus 4 Over c + 3 EndFraction times StartFraction 3 (c squared minus 9) Over c + 2 EndFraction

StartFraction c squared minus 4 Over c + 3 EndFraction times StartFraction c + 2 Over 3 (c squared minus 9) EndFraction

Answer:

I'd love to help, but I need the full question first!!!

Answer:

a = 11

Step-by-step explanation:

Using the Pythagorean Theorem:

[tex] {a}^{2} + {26.4}^{2} = {28.6}^{2} [/tex]

[tex] {a}^{2} + 696.96 = 817.96[/tex]

[tex] {a}^{2} = 121[/tex]

[tex]a = 11[/tex]

Answer:

The relation is  c = 3.519g.

Step-by-step explanation:

This is direct variation.

c = kg     where k is the constant of variation.

Substituting the given values:

190 = k * 54

so the constant of variation is:

k = 190/54 = 3.519   to nearest thousandth,

and  the equation is:

c = 3.519g.

Answer:

A)

Step-by-step explanation:

Given function:  

[tex]h(t)=-16t^2+75t+25[/tex]

The domain (input values) will be the x-intercepts, so the values of t when h(t) = 0.

The quickest way to find these is to use the quadratic formula.

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\implies t=\dfrac{-75 \pm \sqrt{75^2-4(-16)(25)} }{2(-16)}[/tex]

[tex]\implies t=\dfrac{-75 \pm \sqrt{7225}}{-32}[/tex]

[tex]\implies t=\dfrac{75 \pm 85}{32}[/tex]

[tex]\implies t=5, t=-\dfrac{5}{16}[/tex]

Time cannot be negative.

When h(t) = 0, the disk will hit the floor.

Therefore, the domain is restricted to 0 ≤ t ≤ 5

Answer:

Number of maple trees planted = 462

Step-by-step explanation:

Let the number of oak trees planted be x.

Given,

The number of maple trees is 11 times the number of oak trees.

Therefore,

Number of maple trees planted = 11 * x = 11x

Total number of trees planted = Number of oak trees planted + Number of maple trees planted

504 = x + 11x

504 = 12x

x = 504/12 = 42

Number of oak trees planted = x = 42

Number of maple trees planted = 11x = 11 * 42 = 462

Check the picture below.

[tex]p(h)=5000(2)^h\implies \stackrel{p(h)}{100000}~~ = ~~5000(2)^h\implies \cfrac{100000}{5000}=2^h \\\\\\ 20=2^h\implies \log(20)=\log(2^h)\implies \log(20)=h\log(2) \\\\\\ \stackrel{\textit{using the \underline{change of base rule}}}{\cfrac{\log(20)}{\log(2)}=h\implies \log_2(20)=h}\implies 4.3219\approx h[/tex]

The total change in the water in the pool after 2 1/2 hours given the rate of leakage is -3 1/8,

A fraction is a non-integer. It is made up of numerators and denominators. A mixed fraction is made up of a whole number and a proper fraction. An example is 2 1/2.

The total change in the water = -1 1/4 x 2 1/2

= -5/4 x 5/2 = -25/8 = -3 1/8

To learn more about multiplication of fractions, please check: brainly.com/question/1114498

Answer:

A frequency distribution is a table that shows “classes” or “intervals” of data entries with a count of the number of entries in each class.

Step-by-step explanation:

hope this helps you a little!

Answer:

14.3

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2   where a and b are the legs and c is the hypotenuse

14^2 + 3^2 = c^2

196 + 9 = c^2

205 = c^2

Take the square root of each side

sqrt(205) = sqrt(c^2)

14.31782106 = c

Rounding to the nearest tenth

14.3 = c

Answer :

⠀

Explanation :

⠀

Solution :

where,

We know that,

[tex]{\longrightarrow \pmb{\mathbb {\qquad (XZ) {}^{2} = (XY) {}^{2} +( YZ) {}^{2} }}} \\ \\ [/tex]

Now, we will substitute the given values in the formula :

[tex]{\longrightarrow \sf{\pmb {\qquad (XZ) {}^{2} = (3) {}^{2} +( 14) {}^{2} }}} \\ \\ [/tex]

We know that, (3)² = 9 and (14)² = 196. So,

[tex]{\longrightarrow \sf{\pmb {\qquad (XZ) {}^{2} = 9 +196 }}} \\ \\ [/tex]

Now, adding 9 and 196 we get :

[tex]{\longrightarrow \sf{\pmb {\qquad (XZ) {}^{2} = 205 }}} \\ \\ [/tex]

Now, we'll take the square root of both sides to remove the square from XZ :

[tex]{\longrightarrow \sf{\pmb {\qquad \sqrt{(XZ) {}^{2}} = \sqrt{205 }}}} \\ \\ [/tex]

When we take the square root of (XZ)² , it becomes XZ,

[tex]{\longrightarrow \sf{\pmb {\qquad XZ = \sqrt{205 }}}} \\ \\ [/tex]

We know that, square root of 205 is 14.317 (approx) .

[tex]{\longrightarrow { \mathbb{\pmb {\qquad XZ }}}} \approx \pmb{\mathfrak{14.317 } }\\ \\ [/tex]

So,

Answer:

The area of the figure is 385.5 in²

Step-by-step explanation:

The area of the figure = area of hemisphere + area of rectangle

Radius of hemisphere = 10/2 = 5 in

=> 3πr² + length × breadth

=> { 3×(3.14) × 5 × 5} + { 15 × 10 }

=> { 9.42 × 25 } + { 150 }

=> 235.5 + 150

=> 385.5 in²