Solve for x.

logx+log3=log18

The measure of ∠ACD is 150°. So the answer is D.150°.

The ∠ACD is an exterior angle of triangle ABC. We can use the fact that the sum of the measures of the interior angles of a triangle is 180° to solve for the measure of ∠ACD.

Identify the interior angles of triangle ABC: We are given the measures of two interior angles: ∠A = 33° and ∠B = 117°.

Find the sum of the interior angles of triangle ABC: ∠A + ∠B + ∠C = 180°

Substitute the known values and solve for ∠C: 33° + 117° + ∠C = 180°

Combine like terms: 150° + ∠C = 180°

Isolate ∠C: ∠C = 180° - 150°

Calculate the measure of ∠C: ∠C = 30°

Find the measure of ∠ACD: Since ∠ACD is an exterior angle of triangle ABC and ∠C is an interior angle, we know that ∠ACD and ∠C are supplementary angles. Therefore, their measures add up to 180°.

Calculate the measure of ∠ACD: ∠ACD = 180° - ∠C = 180° - 30° = 150°

Therefore, the measure of ∠ACD is 150°. So the answer is D. 150°.

Step-by-step explanation:

Write the population of florida in expanded form using exponents

floride population = 18,801,310

Expanded form ;

1x10^{7} + 8x10^{6} + 8x10^{5} + 0x10^{4} + 1x10^{3} + 3x10^{2} + 1x10^{1} + 0x10^{0}      

the 4 because it's in the hundred place value

I THINK THAT"S HOW YOU DO IT, BUT YOU KNOW JUST TRYING TO HELP YOU :)

Answer:

he has 80 cents

Step-by-step explanation:

dime=10 cents

I'm guessing that the hidden question is how many dimes does Omar have? because this is the first thing I asked myself when solving this equation.

So how many dimes does Omar have?

5 + 3 = 8

Now we know that one dime = 10 cents, so to find the amount of money in cents, all we need to do is multiply 8 * 10

8 * 10 = 80

Omar has 80 cents

Answer:

Step-by-step explanation:

The formula of an area of a rectangle:

[tex]A=l\cdot w[/tex]

l - length (base)

w - width (height)

We have l = 12mm, h = 14mm.

Substitute:

[tex]A=(12)(14)=168\ (mm^2)[/tex]

Answer:

n = 3

Step-by-step explanation:

find multiples of the product of 24 that comes from 6*4

Answer:

6 and 4

2 and 12

1 and 24

3 and 8

Step-by-step explanation:

Answer:

1, 2, 3, 4, 6, 8, 12, 24.

Step-by-step explanation:

The question is basically saying "what are the factors of 24?"

Hello ;w;

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

f=

x=(2x - 5)^2

f=

-4 = -4

I believe your answer is -4, sorry if I'm wrong, have a great day.❤

Answer:

false

Step-by-step explanation:

a natural number is a number you count by, you wouldn't cound by decimals or fractions

Answer: 35 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

60

Answer: 9

Step-by-step explanation:

6 divided by 2/3 = 9

In 6 cups of cereal, there are 9 servings of 2/3 cup.

To find out how many 2/3-cup servings are in 6 cups of cereal, we need to divide the total cups of cereal by the size of each serving. In this case, we divide 6 by 2/3. To divide a whole number by a fraction, we can multiply the whole number by the reciprocal of the fraction. The reciprocal of 2/3 is 3/2, so we have 6×3/2 = 9 cups in total. Therefore, there are 9 servings of 2/3 cup in 6 cups of cereal.

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Answer: Steroids Linked to Higher Heart Disease Risk. High Doses May Raise Risk of Heart Attack, Stroke, Study Shows. By Miranda Hitti. Nov. 15, 2004 -- Taking high doses of steroids (glucocorticoids) seems to increase the risk of heart disease including heart attack, heart failure, and stroke, according to new research.

Step-by-step explanation:

Answer:

high dosages of steroids can cause heart disease and increase the risk of heart attack, heart failure, and stroke.

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

The raise in her hourly pay is

$25.48-$24.50 =$0.98

Cross multiplying (rule of three)

24.50------100%

0.98--------x%

and so, x= 0.98*100/24.5 = 4%

Answer:  The required percent change is 4%.

Step-by-step explanation:  Given that Ayodele received a raise in her hourly pay, from $24.50 to $25.48.

We are to find the percent change.

The percent change is given by

[tex]p=\dfrac{\textup{increse in the amount}}{\textup{original amount}}\times100\%.[/tex]

In the given situation, we have

[tex]\textup{increase in the amount}=\$(25.48-24.50)=\$0.98.[/tex]

Therefore, the percent change is given by

[tex]p=\dfrac{0.98}{24.50}\times100\%=\dfrac{98}{24.50}\%=4\%.[/tex]

Thus, the required percent change is 4%.

Answer:

[tex]y= \frac{-5}{2}x-1[/tex]

Step-by-step explanation:

the line equation is  5x + 2y = 12

Solve for y to find out slope m

y=mx+b

[tex]5x + 2y = 12[/tex]

Subtract 5x from both sides

[tex]2y =-5x+12[/tex]

Divide both sides by 2

[tex]y=\frac{-5}{2} x+6[/tex]

slope = -5/2

Slope of parallel lines are same . So slope of parallel line is [tex]\frac{-5}{2}[/tex]

m=-5/2 , point (-2,4)

[tex]y-y_1= m(x-x_1)[/tex]

[tex]y-4= \frac{-5}{2}(x+2)[/tex]

[tex]y-4= \frac{-5}{2}x-5[/tex]

Add 4 on both sides

[tex]y= \frac{-5}{2}x-1[/tex]

Answer:

Answer is A

Step-by-step explanation:

Trust the process

Answer:

The length of the longer rope piece is 14 ft

Step-by-step explanation:

Let

x -----> the longer piece

y ----> the shorter piece

we know that

The sum of the longer piece plus the shorter piece must be equal to the length of the original piece

x+y=21

y=(21-x) -----> equation A

3x-7=5y ----> equation B

substitute equation A in equation B and solve for x

[tex]3x-7=5(21-x)\\3x-7=105-5x\\5x+3x=105+7\\8x=112\\x=14\ ft[/tex]

therefore

The length of the longer rope piece is 14 ft

Answer:

4410 cards, 9 albums

Step-by-step explanation:

Number of cards in a box = 315

Number of boxes = 14

b) Total number of cards =  Number of boxes × Number of cards in 1 box

=[tex]315\times 14 = 4410[/tex]

a) Carmella estimated she had 3,000 cards so she bought a 6 album of 500 cards.

No, 6 albums are not enough as she estimated wrong number of cards. There are total of 4410 cards but she estimated it to be 3000 cards.

c) Total number of albums required = [tex]\displaystyle\frac{\text{Total number of cards}}{\text{Number of card 1 album can hold}}[/tex]

[tex]=\frac{4410}{500} = 8.82 \approx 9[/tex]

Thus, she will require 9 albums to put all her cards.

Answer:

D(-1,0)

Step-by-step explanation:

Plot points A(-3, 2), B(-1, 4), and C(1, 2) on the coordinate plane (see attached diagram).

Two sides AB and BC are of equal length and are perpendicular, because

[tex]AB=\sqrt{(-3-(-1))^2+(2-4)^2}=\sart{(-2)^2+(-2)^2}=\sqrt{4+4}=2\sqrt{2}\ units\\ \\BC=\sqrt{(-1-1)^2+(4-2)^2}=\sart{(-2)^2+2^2}=\sqrt{4+4}=2\sqrt{2}\ units\\ \\\text{Slope AB}=\dfrac{4-2}{-1-(-3)}=\dfrac{2}{2}=1\\ \\\text{Slope BC}=\dfrac{2-4}{1-(-1)}=\dfrac{-2}{2}=-1\\ \\\text{Slope AB}\cdot \text{Slope BC}=1\cdot (-1)=-1\Rightarrow \text{lines AB and BC are perpendicular}[/tex]

If the quadrilateral ABCD has all sides perpendicular, then ABCD is a square. The diagonals of the square bisects each other. Find the coordinates of the point of intersection of these diagonals. This is the midpoint of segment AC:

[tex]x=\dfrac{-3+1}{2}=-1\\ \\y=\dfrac{2+2}{2}=2[/tex]

If point O(-1,2) is the point of intersection of diagonals, then it is the midpoint of the diagonal BD. Find coordinates of point D:

[tex]x_O=\dfrac{x_B+x_D}{2}\Rightarrow -1=\dfrac{-1+x_D}{2},\ -1+x_D=-2,\ x_D=-1\\ \\y_O=\dfrac{y_B+y_D}{2}\Rightarrow 2=\dfrac{4+y_D}{2}, 4+y_D=4,\ y_D=0[/tex]

Thus, D(-1,0)

Answer:

a. Number of flour cups needed = 4 cups

b. Number of cookies that can be baked = 240 cookies

Explanation:

We are given that:

1 cup of flour is needed to make 2 dozen cookies

To solve the two parts of this question, we will simply use cross multiplication

Part a:

1 cup of flour .......................> 2 dozen cookies

x cups of flour ....................> 8 dozen cookies

[tex]x = \frac{8*1}{2} = 4[/tex] cups

Therefore, 4 cups of flour are required to make 8 dozen cookies

Part b:

1 cup of flour .................> 2 dozen cookies

10 cups of flour ............> y dozens of cookies

[tex]y=\frac{10*2}{1} = 20[/tex] dozens of cookies

This means that, 10 cups of flour can make 20 dozen cookies

However, here we are asked about the number of cookies, not the number of dozens

We know that 1 dozen contains 12 parts

This means that:

1 dozen cookies = 12 cookies

Therefore:

20 dozens cookies = 20 × 12 = 240 cookies

Hope this helps :)

Answer:8

Step-by-step explanation: add 3 on both sides to cancel it from the left, and then x=8.

Answer:

12

Step-by-step explanation:

divide 100 by 8

Answer: 8/3

Step-by-step explanation: To add like fractions, or fractions that have the same denominator, simply add the numerators and keep the original denominator.

Answer:

The answer would be <

Step-by-step explanation:

(18-3)÷(6-1)

18-3=15

6-1=5

15÷5=3

________

4×(10-3)-4×2

10-3=7

4×7-4×2

28-8=20

Answer:the answer is 24

Step-by-step explanation:

Because when 18 is the half of 36 so 24 is the half of 48

Given x and y vary directly with constant ratio 1.33, the value of x when y equals 18 is 23.94.

The subject question deals with direct variation, a concept in Mathematics. When two variables vary directly, a change in one variable results in a proportionate change in the other variable. If x and y vary directly, it means the ratio of x to y is constant.

From the problem, x = 48 when y = 36. Therefore, the ratio of x to y is 48/36 = 1.33.

To find the value of x when y = 18, simply multiply the constant ratio (1.33) by the new value of y.

So, x = 1.33 * 18 = 23.94

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Answer:

[tex]Log_{(3)}X[/tex]

Step-by-step explanation:

[tex]f(x)=3^{X}[/tex]

[tex]y=3^{X}[/tex]

exchange the variables x and y

[tex]X=3^{y}[/tex]

[tex]Log_{(3)}X=Log_{(3)}3^{y}[/tex]

[tex]Log_{(3)}X=y[/tex]

[tex]f^{-1}(x)=Log_{(3)}X[/tex]

Answer:

subtraction= Mike is selling 50 apples. Kenny is selling 30 apples,"how many more" apples does mike have than ken?

50- 30 = 20

mike has 20 "more" apples than ken.

there are 15 kindergarteners, "but only" 10 chairs, "how many" chairs would the teachers have to "take away" from the room next door?

15- 10=5

Answer:

[tex]3x^2-3x-60[/tex]

Step-by-step explanation:

Given: [tex]3(x+4)(x-5)[/tex]

Let's use the distributive property to multiply [tex](x+4)(x-5)[/tex] together since they are right next to each other. We can use the FOIL method.

[tex](x+4)(x-5)\\x^2-5x+4x-20\\x^2-x-20[/tex]

Now that we simplified that, we still have to multiply everything by the value of [tex]3.[/tex]

[tex]3(x^2-x-20)\\3x^2-3x-60[/tex]

Now, you could have left the answer as [tex]3(x^2-x-20)[/tex] since it is factored, but the problem wants us to find the product, so we need to completely simplify.

Answer:

(12,10)

Step-by-step explanation:

Answer:

second one diagram rotated 120

In a 120° counterclockwise rotation about point B, diagram AABC would shift each point along a circular path 120° in a counterclockwise direction around point B. The positions of points A and C would change, while point B would stay as it is. The correct diagram would reflect these changes.

Without a specific diagram to refer to, I can provide only a general explanation of how to determine the diagram that represents AABC rotated 120° counterclockwise about point B.

Rotations in a plane are performed counterclockwise with a positive degree measure. So, a 120° counterclockwise rotation about a fixed point B would take every point on triangle AABC and shift it along a circular path 120° in a counterclockwise direction around point B. The result would be a new triangle A'B'C'. If point B is the origin of rotation, it would remain unchanged. However, points A and C would change their positions after the rotation.

To determine the correct diagram, you would look for a triangle that has been shifted around point B in a counterclockwise direction with positions of points A and C reflecting a 120° rotation.

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