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Answer:

ST = 8 m

SU = 7 m

m∠Q = 75°

m∠S = 59°

m∠R = 46°

m∠U = 46°

Step-by-step explanation:

The given parameter are;

ΔPQR is congruent to ΔSTU

In ΔPQR, m∠P = 59°, PR = 8 m, PQ = 7 m

In ΔSTU, m∠T = 75°

By Side-Angle-Side rule of congruence, and given that m∠P ≠ m∠T, we can have;

m∠S ≅ m∠P, by Congruent Parts of Congruent Triangles are Congruent, CPCTC

ST ≅ PR, SU ≅ PQ, m∠Q ≅ m∠T, m∠U ≅ m∠R

Therefore;

ST = PR = 8 m

ST = 8 m

SU = PQ = 7 m

SU = 7 m

m∠Q = m∠T = 75°

m∠Q = 75°

m∠S = m∠P = 59°

m∠S = 59°

m∠U = m∠R = 180 - (75° + 59°) = 46°

m∠R = 46°

m∠U = 46°.

The original number of marbles in the bag is 30.

The given parameters are:

[tex]Red = x + 1[/tex]

[tex]Total = x^2 + 5[/tex]

The probability of red is:

[tex]P(Red) = \frac{Red}{Total}[/tex]

[tex]P(Red) = \frac{x+1}{x^2 + 5}[/tex]

When 20 marbles were removed, the marbles left are:

[tex]Marbles =Total - 20[/tex]

This gives:

[tex]Marbles =x^2 + 5 - 20[/tex]

[tex]Marbles =x^2 -15[/tex]

The probability of selecting a scratched marble at this point is:

[tex]P(Scratch) = \frac{Scratch}{Marbles}[/tex]

[tex]P(Scratch) = \frac{x -3}{x^2 - 15}[/tex]

This probability equals the probability of red.

i.e.

[tex]P(Red) = P(Scratch)[/tex]

So, we have:

[tex]\frac{x +1}{x^2 + 5} = \frac{x -3}{x^2 - 15}[/tex]

Cross multiply

[tex](x + 1)(x^2 - 15) = (x - 3)(x^2 + 5)[/tex]

Expand

[tex]x^3 - 15x + x^2 - 15 = x^3 + 5x - 3x^2 - 15[/tex]

Subtract [tex]x^3[/tex] from both sides

[tex]- 15x + x^2 - 15 = 5x - 3x^2 - 15[/tex]

Add 15 to both sides

[tex]- 15x + x^2 = 5x - 3x^2[/tex]

Collect like terms

[tex]3x^2 + x^2 - 15x - 5x = 0[/tex]

[tex]4x^2 - 20x = 0[/tex]

Divide through by 4

[tex]x^2 - 5x = 0[/tex]

Expand

[tex]x(x - 5) = 0[/tex]

Split

[tex]x = 0[/tex] or [tex]x - 5 = 0[/tex]

[tex]x = 0[/tex] or [tex]x = 5[/tex]

x can't be 0.

So: [tex]x = 5[/tex]

The number of marbles initially is:

[tex]Total = x^2 + 5[/tex]

[tex]Total = 5^2 + 5[/tex]

[tex]Total = 30[/tex]

Hence, the original number of marbles in the bag is 30.

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Answer:

See the diagram below:

                             Red  3/8  -----------------> Red-Red  = 4/9*3/8 = 1/6

Red 4/9            <

                            Orange 5/8 --------------> Red-Orange = 4/9*5/8 = 5/18

                            Red 4/8 --------------------> Orange-Red = 5/9*4/8 = 5/18

Orange 5/9      <

                           Orange 4/8 ----------------> Orange-Orange = 5/9*4/8 = 5/18

Answer:

25x^2 +40x+16

Step-by-step explanation:

(5x + 4)²​

(5x+4)(5x+4)

FOIL

first  5x*5x = 25x^2

outer  5x*4 = 20x

inner 4*5x = 20x

last = 4*4 = 16

Add them together

25x^2 +20x+20x+16

Combine like terms

25x^2 +40x+16

Answer:

[tex] {(5x + 4)}^{2} \\ = {(5x)}^{2} + 2 \times 4 \times 5x + {4}^{2} \\ = 25 {x}^{2} + 40x + 16 \\ thank \: you[/tex]

Answer:

<A = 51

Step-by-step explanation:

Since AB = AC  ( shown by the lines on the sides) we know that this is an isosceles triangle

Since the sides are the same, the base angles are the same

<A = <C

<C = 51 so <A = 51

Answer:

a)

i) Interquartile range is   2.4  

ii) Upper boundary is 10.8  

The Lower boundary is 1.2  

iii) Outliers are points above the upper boundary or below the lower boundary  

There is one outlier: 1.1

b) The modified boxplot with one outlier is given in the diagram.                                                          

c) The 80th percentile is    

The minimum rating the hotel can get is 7.3

Step-by-step explanation:

a)

i) Interquartile range is  

IQR = Q3-Q1 = 7.2-4.8 = 2.4  

ii) Upper boundary = Q3+ 1.5 *IQR = 7.2+1.5*2.4 = 10.8  

Lower boundary = Q1 - 1.5*IQR = 4.8- 1.5*2.4 = 1.2  

iii) Outliers are points above the upper boundary or below the lower boundary  

There is one outlier: 1.1  

c) The 80th percentile is given by  

n= 12  

k = 0.80  

Index is given by k*n =0.80*12 = 9.6  

Round to nearest whole number, that is 10th  

80th percentile is the 10th number (arranged in ascending order)  

80th percentile = 7.3  

The minimum rating the hotel can get is 7.3.

b) The modified boxplot with one outlier is given as follows,  

Answer:

Solution given:

[tex]\sqrt{6-15x} =5x+d[/tex]......(1)

d=?

and

x=-2

Substituting value of x in equation 1.

[tex]\sqrt{6-15*-2} =5*-2+d[/tex].

Solve the like terms

[tex]\sqrt{6+30} =-10+d[/tex].

solve the like terms

[tex]\sqrt{36} =-10+d[/tex].

we have square root of 36 is 6.

6=-10+d

d=16

the value of constant term is 16.

The value of d for the expression [tex]\sqrt{6-15x} = 5x+d[/tex] is 16.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The value of 'd' is calculated as,

[tex]\sqrt{6-15x} = 5x+d[/tex]

Put the value of x =-2,

[tex]\sqrt{6-(15\times -2)}=(5\times -2)+d[/tex]

√36 = -10 + d

6 = -10 + d

d = 16

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Answer:

Pentagon = 72°

Octagon = 45°

Step-by-step explanation:

To solve for the measure of one exterior angle in a regular pentagon;

n = number of sides

180 - (180 x n-2/n)

180 - (180 x 5-2/5)

180 - (180 x 3/5)

180 - (540/5)

180 - 108

Exterior angle = 72°

To solve for the measure of one exterior angle in a regular octagon;

n = number of sides

180 - (180 x n-2/n)

180 - (180 x 8-2/8)

180 - (180 x 6/8)

180 - (1080/8)

180 - 135

Exterior angle = 45°

Answer:

Step-by-step explanation:

1.68/6=0.28 per pencil in pack 1

2.34/9 =0.26 per pencil in pack 2

So pack 2 is better in terms of Maths

But in business, people prefer pack 1

Answer:

1/2×2×12=12 feet

Step-by-step explanation:

1/2× base area × height

Answer:

180 degrees

Step-by-step explanation:

ABCD is now opposite where it started, so it was rotated 180 degrees

I hope this helps!

Answer:

180 degrees

Step-by-step explanation:

Answer:

550

Step-by-step explanation:

To round 553 to the tens place, we would need to identify the value of the digit in the ones place.

If the digit in the ones place is greater than 5, we increase the tens place by 1 & convert the ones place into a 0.

If not, we leave the tens place as is & convert the ones place into a 0.

Since 3 is less than 5, we round 553 to 550 so you are correct.

Answer:

Yes

550 has 2 sig figs

553 has 3

Step-by-step explanation:

Answer:

[tex] \frac{ {11}^{56} }{ {5}^{18} } [/tex]

Step-by-step explanation:

[tex] {55}^{56} \times {5}^{22} \times {5}^{ - 96} [/tex]

[tex] = {55}^{56} \times {5}^{ - 74} [/tex]

[tex] = {11}^{56} \times {5}^{56} \times \frac{1}{ {5}^{74} } [/tex]

[tex] = {11}^{56} \times \frac{1}{ {5}^{18} } [/tex]

[tex] = \frac{ {11}^{56} }{ {5}^{18} } [/tex]

Hi

P and Q only intersect for 2 as 2 is common for P and Q . So P U Q = 2

For the diagram :

One big circle name U with 1 on the

Far corner left and 9 on the far right corner.

Then on the left, a circle within circle U with the number Of P

Same with Q on the right.

But P and Q must intersect on number 2 as 2 is in both circles.

ps : nothing oblidge you to set the number on mathematical order. Of it'esasier to do the circles, do it whatever you like as long as you respect what is said.

Answer:

There are 3 numbers that are not whole numbers.

3/4, 3.7, and sqrt 3 are not whole numbers

Answer:

3

Step-by-step explanation:

There are only 3 that aren't whole numbers. The whole numbers are: 32, 1,265, 3000, and 1. The numbers that aren't whole are: 3/4, 3.7, and √3

Answer:

D

Step-by-step explanation:

Change=Temperature/Time

Change=(-49/4)/(7/2)

Answer:

$0.60

Step-by-step explanation:

Find the unit rate.

[tex]\frac{Dollars}{Cookies}=\frac{9}{15}[/tex] ÷ [tex]\frac{15}{15}=\frac{0.6}{1}[/tex]

Therefore, the cost for one cookie is $0.60.

Answer:

$0.60

You need to find the unit rate. Unit rate is a ratio of 1 to another number, written like 1 : ?.

If a box of 15 cookies costs $9, and you want to find the price of one cookie, then you will need to use unit rate.

Start with the ratio of cookies to dollars.

15:9

Now, you need to find out the cost of one cookie. To do this, you will need to divide 9 by 15 (9/15) because you're trying to split 9 into 15 cookies.

But, you can't have .6 dollars, so the answer will be $0.60, or 60 cents.

B..The discriminant is equal to 0, which means equation has on real number solutions

The discriminant is equal to 0, which means the equation has one real number solution, option B is correct.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The discriminant of a quadratic equation in standard form, ax² + bx + c = 0, is given by the expression b² - 4ac.

The given equation is -2x² = -8x+8

a = -2, b = 8, and c = -8.

Substituting these values into the formula for the discriminant, we get:

b² - 4ac = (8)² - 4(-2)(-8)

= 64 - 64

= 0

Therefore, the discriminant is equal to 0.

When the discriminant is equal to 0, it means that the quadratic equation has one real number solution (a double root) because the quadratic formula will give only one root.

Hence,  the discriminant is equal to 0, the equation -2x² = -8x + 8 has one real number solution.

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Answer:

1 1/6

Step-by-step explanation:

1/3 - (-5/6)

Subtracting a negative is like adding

1/3 + 5/6

Get a common denominator of 6

1/3 *2/2 + 5/6

2/6 + 5/6

7/6

6/6 + 1/6

1 1/6

Answer: -1 1/6

Step-by-step explanation: -5/6 - 1/3 (2/2) -5/6 - 2/6 -7/6 -1 1/6

Answer:

The answer is 119

Step-by-step explanation:

Just count, but I did it a different way but multiplying then subtracting.

Answer:

Dilation of 1/2 means we have to multiply the number by 1/2

V' (-2,1)

U' (1,3)

E' (0,1)

Hope it helps :)

Answer:

zero of the function occurs at x = -6

Step-by-step explanation:

Given f(x) = -4(x+3)+6(x+4)

Since the question is incomplete, we can as well find the zero of the given function. The zero exists when f(x) = 0

Hence;

-4(x+3)+6(x+4) = 0

Expand

-4x - 12 + 6x + 24 = 0

Collect the like terms

-4x + 6x - 12 +24 = 0

2x + 12 = 0

2x = -12

x = -12/2

x = -6

Hence the zero of the function occurs at x = -6

Answer:

Equation of the line is y = 4x + 19

Step-by-step explanation:

slope, m = 4

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

consider (-3, 7):

[tex]7 = (4 \times - 3) + c \\ 7 = - 12 + c \\ c = 19[/tex]

equation:

[tex]y = 4x + 19[/tex]

Answer:

y = 4x + 19

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x - 1 ← is in slope- intercept form

with slope m = 4

Parallel lines have equal slopes, then

y = 4x + c ← is the partial equation

To find c substitute (- 3, 7) into the partial equation

7 = - 12 + c ⇒ c = 7 + 12 = 19

y = 4x + 19 ← equation of parallel line

Answer:

im not sure but i got 30.1

Step-by-step explanation:

[tex] \cos(x) = \frac{45}{52} \\ x = 30.1[/tex]

Answer:

[tex]1.1*10^{-11}[/tex]

I used a calculator.

Answer:

[tex]1.1*10^{-11}[/tex]

Step-by-step explanation:

0.000010*0.00055*0.002= 1.1*10^-11 or basically 0.

Answer:

8.555.... is a irrationtional number .

Step-by-step explanation:

The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.

s

SO, LAST IS CORRECT

?ARK ME AS BRAILIEST

Answer:

hello,

Step-by-step explanation:

[tex]cos(3\theta)+cos(4\theta)\\\\=2*cos(\dfrac{4\theta+3\theta}{2} )*cos(\dfrac{4\theta-3\theta}{2} )\\\\\boxed{=2*cos(\dfrac{7\theta}{2} )*cos(\dfrac{\theta}{2} )}[/tex]

Answer:

the answer will be..

x=-1

x=4

(x+1) (x-4)

but im sorry i dunno what's lesser and greater means

====================================================

Explanation:

At the 60 day mark, the following number of widgets are produced

The fourth plant makes 150 widgets, which is between B and C

We see that the fourth plant does not make more than Plant A, so we can rule out choice A.

The fourth plant does not make less than Plant B, which allows us to rule out choice B.

The only thing left is choice C. Sure enough, this statement is true since 150 widgets made at the fourth plant is less than 300 made in Plant A. This is why choice C is the answer.