Help me with these math questions.......

[tex]10e^{2x}-5=23e^x\qquad\text{subtract}\ 23e^x\ \text{from both sides}\\\\10e^{2x}-23e^x-5=0\\\\10(e^x)^2-23(e^x)-5=0\\\\\text{substitution:}\ e^x=t > 0\\\\10t^2-23t-5=0\\\\10t^2-25t+2t-5=0\\\\5t(2t-5)+1(2t-5)=0\\\\(2t-5)(5t+1)=0\iff2t-5=0\ \vee\ 5t+1=0\\\\2t=5\ \vee\ 5t=-1\\\\t=\dfrac{5}{2} > 0\ \vee\ t=-\dfrac{1}{5} < 0\\\\\text{therefore}\ e^x=\dfrac{5}{2}\to\ln e^x=\ln\left(\dfrac{5}{2}\right)\\\\\boxed{x=\ln\left(\dfrac{5}{2}\right)}[/tex]

Answer:

B is the correct option choice !

The measure of 2 yards in centimeters is 182.88 cm

Using the conversions given:

1 yard = 3 × 12 inches

1 yard = 36 inches

1 yard = 36 × 2.54 cm

1 yard = 91.44 cm

Hence,

For 2 yards : (91.44 × 2) = 182.88 cm

The measure of 2 yards in centimeters is 182.88 cm

Answer:

1) f(x) = -1/2x+1

I'm sorry I don't know the 2nd one...

Step-by-step explanation:

The y-intercept is always plotted first. from there, you go down one, and to the right too. and so one, and in reverse, up one, and left two.

Answer:1. f(x) = -1/2x+1

Answer:

The Rosita investment worth in 2025 is $83486.4 .

Step-by-step explanation:

The expontential increase function is given by.

[tex]y = a(1 + r)^{t}[/tex]

Where a is the initial value , r is the rate of interest in the decimal form and t is the time.

As given

Rosita invested in a precious mineral.

The value of the mineral tends to increase by about 12% per year.

She invests $24,000 in 2014.

As

a = 24000

12% is written in the decimal form.

[tex]= \frac{12}{100}[/tex]

= 0.12

r = 0.12

As Rosita invested from 2014 to 2025.

Than

t = 2025 - 2014

t = 11 years

Put in the expontential increase function.

[tex]y = 24000(1 + 0.12)^{11}[/tex]

[tex]y = 24000(1.12)^{11}[/tex]

y = 24000 × 3.4786 (Approx)

y = $83486.4

Therefore the Rosita investment worth in 2025 is $83486.4 .

q - number of quarters

2q - number of dimes

2q · $0.10 - Amount in dimes

q · $0.25 - Amount in quarters

$9.00 - Total amount

The equation:

[tex]2q(0.1)+q(0.25)=9\\\\0.2q+0.25q=9\\\\0.45q=9\qquad\text{divide both sides by 0.45}\\\\q=20[/tex]

Paul has 20 quarters.

To find quarters does Paul have.

The branch of mathematics dealing with the properties and manipulation of numbers.

Let the q - number of quarters

2q - number of dimes

2q · $0.10 - Amount in dimes

q · $0.25 - Amount in quarters

$9.00 - Total amount

The equation:

2q(0.1)+q(0.25)=9

0.45q=9

q=20

So, Paul has 20 quarters.

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The slope-intercept form:

[tex]y=mx+b[/tex]

We have:

[tex]3x+7y=14[/tex]              subtract 3x from both sides

[tex]7y=-3x+14[/tex]             divide both sides by 7

[tex]\boxed{y=-\dfrac{3}{7}x+2\to\boxed{C.}}[/tex]

Answer:

2x + 3

Step-by-step explanation:

product means to multiply, hence

the product of 2 and a number x = 2 × x = 2x

3 more than means add on 3, thus

expression is 2x + 3

Answer:

One brownie costs $1.25

Step-by-step explanation:

We need to solve this with simultaneous equations. First, write the equations out in two lines:

c = cookies and b = brownies.

10c + 3b = 11.25

6c + 9b = 15.75

We need to make either the two c values the same or the two b values the same. Lets change the two b values to the same by multiplying the first equation by three:

10c + 3b = 11.25

10c * 3 = 30c

3b * 3 = 9b

11.25 * 3 = 33.75

30c + 9b = 33.75

Now we can subtract the second equation from this:

30c - 6c = 24c

9b - 9b = 0

33.75 - 15.75 = 18

24c = 18

Now divide both sides by c to find 1c:

c = 0.75

Now put this back into the first equation:

10(0.75) + 3b = 11.25

7.50 + 3b = 11.25

Move the +7.50 over to the other side making it a negative:

3b = 11.25 - 7.50

3b = 3.75

Divide both sides by 3:

b = 1.25

Answer:

Cost of 72 ounces of grapes is $13.5

Step-by-step explanation:

In order to solve his problem, we first need to get all the values in the same units.

  1 pound = 16 ounces

∴ 6 pounds= 16×6 = 96 ounces

Now by unitary method, we solve the question as follows:

price of 96 ounces of grapes = $ 18

price of 1 ounce of grapes = $ (18÷96)

∴ price of 72 ounces of grapes = $ [(18÷96)×72]

= (0.1875×72) =  $ 13.5

Answer: 6 of the picks would be green

Step-by-step explanation:

[tex]f(x)=5x\\\\\text{The domain:}\ D=\{0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6\, ...\}=\text{Whole numbers}\\\\\text{The range:}\\\\f(0)=5(0)=0\\f(1)=5(1)=5\\f(2)=5(2)=10\\f(3)=5(3)=15\\f(4)=5(4)=20\\f(5)=5(5)=25\\\vdots\\R=\{0,\ 5,\ 10,\ 15,\ 20,\ 25,\ ...\}[/tex]

Answer:

C

Step-by-step explanation:

We can find the surface area of the dumbbell by adding the surface areas of each part. We have two equal round ends of the dumbbell to count and the skinnier inside. Each is a cylinder and each can be found by finding the area of the base (times 2 for two bases) and adding it to the circumference times the height.

[tex]2(\pi r^{2} )+(\pi d)h[/tex]

Dumbbell Ends

There are two ends and so we will count this measurement twice. The diameter is 12.5. The radius is half of this and is 6.25. The height is 8.

[tex]2(\pi r^{2} )+(\pi d)h[/tex]

[tex]2(\pi (6.25)^{2} )+(\pi 12.5)8[/tex]

[tex]2(\pi 39.0625 )+(\pi 100[/tex]

245.4369+314= 559.43

But we must count is twice, so 559.43(2)=1118.87 cm squared.

Dumbbell Middle

The diameter is 2.50. Radius is 1.25. The height is 10.5. The ends actually don't show because they are attached. So we will only calculate the second part and add it to the other.

[tex](\pi 2.5)10.5[/tex]=82.47

82.47+1118.87=1201.33 cm squared.

Why is this too large? Why isn't it an answer choice? Because the ends of the middle don't show, they also take up that much area on other side. They are not part of the surface area and they make it smaller. So we will subtract that area now.

[tex]2(\pi 1.25^{2} )[/tex]=9.817

1201.33-9.817=1191.84 cm squared.

Answer:

true/ true/ false/ true

Step-by-step explanation:

4x² is a term in both the numerator and denominator → Correct

factorise numerator and denominator

4x² - 4 = 4(x² - 1) ← common factor of 4

x² - 1 ← is a difference of squares and factors as

(x - 1)(x + 1)

4x² - 3x - 1 = (4x + 1)(x - 1) ← in factored form

Hence (x - 1) is a common factor in the numerator and denominator → Correct

4 is only a common factor in the numerator not the denominator

the denominator has three terms → Correct

being 4x² , - 3x and - 1

Answer: 8 miles per hour

Step-by-step explanation:

30 + 30 = 60, 60 minuets in an hour  4 + 4 = 8. 8 miles per hour hope i helped :)

Answer:

8 miles!

Step-by-step explanation:

30 + 30 = 60, 60 minutes in an hour and  4 + 4 = 8. So the answer is 8 miles per hour

Hope this helps!

Answer: WZ

The sequence ABCD has AD as the first and last letters of that sequence, so this pattern applies to WXYZ as well to pull out WZ. Angle A pairs up with angle W because they are both the first letters of the sequences. These angles are congruent from the fact that the parallelograms are similar. The same can be said for angle D and angle Z.

note: WZ is the same as ZW. The order doesn't matter when it comes to labeling segments based on endpoints.

Answer:

-2-p

Step-by-step explanation:

(p-2)x=4-p^2

(4-p^2)/(p-2)

-2-p

The solution of the expression for the given condition would be, - (p + 2).

Used the concept of trigonometry formula which stated that,

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

Let us assume that,

When we multiply by x in (p - 2) the solution is (4 - p²).

So, it can be written in mathematical form as,

[tex]x \times (p - 2) = (4 - p^2)\\[/tex]

[tex]x \times (p - 2) = (2^2 - p^2)\\[/tex]

[tex]x \times (p - 2) = (2 - p) (2 + p)[/tex]

[tex]x \times (p - 2) = - (p - 2) (2 + p)[/tex]

Divide both sides by (p - 2),

[tex]x = - (p + 2)[/tex]

So, we get;

[tex](p - 2) \times - (p + 2) = (4 - p^2)[/tex]

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Answer:

Our answer is [tex]x=-2+\sqrt{2}[/tex].

Step-by-step explanation:

To solve for x, we need to isolate the variable. We can do so by subtracting 2 to both sides.

[tex]x+2=\sqrt{2} \\x+2-2=-2+\sqrt{2} \\\\x=-2+\sqrt{2} \\[/tex]

Our answer is [tex]x=-2+\sqrt{2}[/tex].

To find the decimal, calculate with a calculator.

Final answer:

The width of the rectangle is calculated using the formula for the perimeter of a rectangle, P = 2l + 2w. Given a perimeter of 66 cm and a length of 24 cm, the width is found to be 9 cm.

Explanation:

The question is asking to find the width of a rectangle given the perimeter and the length. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

To find the width, we can rearrange the formula: w = (P - 2l) / 2.

Substituting the given values into the formula:

w = (66 cm - 2 * 24 cm) / 2

w = (66 cm - 48 cm) / 2

w = 18 cm / 2

w = 9 cm

Therefore, the width of the rectangle is 9 cm.

Answer:

The answer is 823,054,658,786.

Step-by-step explanation:

Add all of them together.

Answer:

Step-by-step explanation:

Question 4:

  Statement                                           Reason

1. [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect at O                    1. Given

2. O is the midpoint of [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex]   2. Definition of bisector

3. [tex]\overline{AO}[/tex] ≅ [tex]\overline{CO}[/tex] and [tex]\overline{BO}[/tex]  ≅ [tex]\overline{DO}[/tex]                3. Definition of midpoint

4. ∠AOB ≅ ∠COD                                4. Vertical Angle theorem

5. ΔAOB ≅ ΔCOD                                5. SAS postulate

6. ∠A ≅ ∠C                                           6. CPCTC

*****************************************************************************

Question 5:

  Statement                                    Reason

1.  [tex]\overline{BD}[/tex] ≅ [tex]\overline{BC}[/tex] and [tex]\overline{AD}[/tex] ≅ [tex]\overline{CD}[/tex]         1. Given

2. [tex]\overline{BD}[/tex] ≅ [tex]\overline{BD}[/tex]                                 2. Reflexive Property

3. ΔABD ≅ ΔCBD                         3. SSS Postulate

4. ∠1 ≅ ∠2 and ∠3 ≅ ∠4               4. CPCTC

5. [tex]\overline{BD}[/tex] bisects ∠ABC and ∠ADC  5. Definition of angle bisector

Answer:

EF = 5 units

Step-by-step explanation:

If ΔABC and ΔDFE are congruent, then

AB = DF

BC = FE

CA = ED

and

angles A and D are congruent

angles B and F are congruent

angles C and E are congruent

Answer:

see explanation

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x , y) → (y , - x)

Answer:The answer is choice C. and the rotation is 180

Step-by-step explanation:i just got it right

Answer:

$1,250

Step-by-step explanation:

We can write a proportion to find the total amount using the information given. A proportion is two equivalent ratios set equal to each other. If 1200 is 4% less than last year, it's 96% of what he raised last year.

[tex]\frac{96}{100}=\frac{1200}{y}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

96(y)=100(1200)

96y=120000

y=1250

Answer:

Choice C --- It intersects the x-axis at the same angle as line m

Step-by-step explanation:

Check out the attached image below for an example. In this example, both lines form a 30 degree angle with the x-axis. These two angles are congruent due to the corresponding angle theorem. This is the idea where two parallel lines form congruent angles such that they are in the same corresponding position.

Answer:

the answer is c

Step-by-step explanation:

Jenny's profit per bracelet is about $1.22. If she sells all 45 bracelets, her total profit is approximately $54.77.

The subject of this question is profit, which in this case will occur when Jenny is able to sell her bracelets for more than she paid for the materials to make them. She pays $12.75 for the materials to make 45 bracelets, meaning each bracelet costs her $12.75 / 45 = $0.283 to make. If she sells each bracelet for $1.50, that means she earns $1.50 - $0.283 = $1.217 in profit for each bracelet. If she sells all 45 bracelets, her total profit would therefore be $1.217 * 45 = $54.765. However, since we typically round money to the nearest cent, her total profit will be approximately $54.77.

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You probably already have an idea of what a matrix is; it's a rectangular array of numbers. What they represent is a bit complicated to explain. There's a whole subject about it (see "linear algebra" for more info). Whatever they represent isn't important though, you don't need to know everything about matrices to compute their product (or whether it's even possible).

A quick definition: A matrix of dimension [tex]r[/tex]-by-[tex]c[/tex] is a matrix with [tex]r[/tex] rows and [tex]c[/tex] columns.

Matrix multiplication all comes down to an operation called the "dot product". It's defined by the sum of component-wise products of elements between two lists. What this means is, if [tex]x=\{1,2,0\}[/tex] and [tex]y=\{-1,0,3\}[/tex], then the dot product of [tex]x[/tex] and [tex]y[/tex] is

[tex]x\cdot y=(1)(-1)+(2)(0)+(0)(3)=-1+0+0=-1[/tex]

What we did was take the first elements of each list and multiplied them, and the same for the other two elements, then added them all together. Notice that the product can't be computed if [tex]x[/tex] and [tex]y[/tex] don't thave the same number of elements.

We write this product in matrix form as

[tex]\begin{bmatrix}1&2&0\end{bmatrix}\begin{bmatrix}-1\\0\\3\end{bmatrix}[/tex]

Notice the pattern here: on the left, a matrix with 1 row and 3 columns; on the right, a matrix with 3 rows and 1 column. The number of columns of the first matrix have to match the number of rows of the second.

The orientation makes a big difference. The product above returns a 1-by-1 matrix (or simply a scalar number):

[tex]\begin{bmatrix}1&2&0\end{bmatrix}\begin{bmatrix}-1\\0\\3\end{bmatrix}=\begin{bmatrix}(1)(-1)+(2)(0)+(0)(3)\end{bmatrix}=\begin{bmatrix}-1\end{bmatrix}=-1[/tex]

On the other hand, the alternate orientation would result in a 3-by-3 matrix.

[tex]\begin{bmatrix}1\\2\\0\end{bmatrix}\begin{bmatrix}-1&0&3\end{bmatrix}=\begin{bmatrix}(1)(-1)&(1)(0)&(1)(3)\\(2)(-1)&(2)(0)&(2)(3)\\(0)(-1)&(0)(0)&(0)(3)\end{bmatrix}=\begin{bmatrix}-1&0&3\\\-2&0&3\\0&0&0\end{bmatrix}[/tex]

So the number of rows of the first matrix and number of columns of the second matrix determine the number of rows and columns, respectively, of the matrix product.

I think we have enough information about matrix multiplication to answer this question. If [tex]A[/tex] has dimensions [tex]m\times n[/tex] and [tex]B[/tex] has dimensions [tex]n\times p[/tex], then the matrix product [tex]AB[/tex] exists ([tex]n[/tex] columns in [tex]A[/tex], [tex]n[/tex] rows in [tex]B[/tex]), but the matrix product [tex]BA[/tex] does not ([tex]p[/tex] columns in [tex]B[/tex], [tex]m[/tex] rows in [tex]A[/tex], but [tex]m\neq p[/tex]). So I is not true.

We know [tex]AB[/tex] exists, and with [tex]m[/tex] rows in [tex]A[/tex] and [tex] p[/tex] columns in [tex]B[/tex], we expect [tex]AB[/tex] to have [tex]m[/tex] rows and [tex]p[/tex] columns, so [tex]AB[/tex] has dimensions [tex]m\times p[/tex]. So II is true.

With dimensions [tex]r\times c[/tex], a matrix would contain [tex]rc[/tex] elements. [tex]m,n,p[/tex] are distinct, so [tex]mp\neq n^2[/tex]. So III is not true.

Answer:  The correct option is

(d) I and II only.

Step-by-step explanation:  Given that matrix A has dimensions m x n and matrix B has dimensions n x p where m, n, and p are distinct positive integers.

We are to select the one that is true from the following :

I.   the product of BA doesn't exist

II.  the product of AB exists and has dimensions m x p

III. the product of AB exists and has dimensions n x n

We know that two matrices X and Y can be multiplied if the number of columns in X is equal to the number of rows in Y.

Also, if X has dimensions  a x b and Y has dimensions b x c, then the product XY is possible and it has dimensions a x c. Also, the product YX doesn't exist.

So, for the given matrices A and B, the following points are true :

(I) the product of BA doesn't exist.

(II) the product of AB exists and has dimensions m x p.

Thus, only I and II are TRUE.

Option (d) is CORRECT.

When the pack of 80 stickers is divided evenly among the three friends, each friend receives 26 stickers, with the remaining 2 stickers going to their teacher.

In order to find out how many stickers each friend will get from a pack of 80, we can divide the total number of stickers by the number of friends. In this case, that's 80 stickers ÷ 3 friends. This division gives us a result of 26 stickers with a remainder of 2.

However, the question states that the remainder is given to their teacher. So while the remainder division resulted in each friend getting 26 stickers with an extra 2 left over, those extra 2 stickers are given to the teacher. Therefore, each friend ends up with 26 stickers.

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Answer:

(12) A

(14) A

(15) E

hope this help

Step-by-step explanation: