Factor the polynomial.

X2+3x-54

Step-by-step explanation:

x²-8x+15= 0

x²-2*1*4*x+ 16-1=0

x²-2*1*4*x+4² = 1

(x-4)² = 1

x-4 =1   or x-4= -1

x= 5      or x=3

so the solutions are 5 and 3

r²+18r+56=0

r²+2*1*9*r+ 81-25=0

r²+2*1*9*r+9² = 25

(r+9)² = 25

r+9 = 5  or r+9 = -5

r= -4  or   r = -14

so the solutions are -4 and -14

x²+2x-24=0

x²+2*1x +1-25=0

x²+2*1*x+1² = 25

(x+1)² = 25

x+1= 5  or x+1= -5

x = 4 or   x= -6

so the solutions are 4 and -6

p²+12p-54 = 0

p²+2*6*p+36-90=0

p²+2*6*p+6² = 90

(p+6)² = 90

p+6 = √90 or p+6 = -√90

p = √90-6  or p=  -√90-6

m²-6m-55= 0

m²-2*3*m+3²-64=0

(m-3)² = 64

m-3 = 8 or m-3 = -8

m= 11 or m= -5

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

Explanation:

This is a visual example of the pythagorean theorem. We add the areas of the two squares to get

13+29.25 = 42.25

Then we apply the square root to this to get the value of x, which is the hypotenuse of the right triangle

x = sqrt(42.25) = 6.5

---------

Side note: if you're curious about finding the other lengths of the triangle, apply the square root to those areas. The blue area 29.25 will lead to a side length of approximately sqrt(29.25) = 5.4083269; the red square will follow the same idea.

Answer:

Step-by-step explanation:

area of a square=a²

A=29.25

a=side=√29.25 first square

second square =a=√13

find x(c)

right triangle: a²+b²=c²

(√29.25 )²+(√13)²=c²

29.25+13=c²

c=√(29.25+13)=6.5 unit

y^2 + 15y + 56 factors to (y+7)(y+8)

This is because 7+8 = 15 is the middle term and 7*8 = 56 is the last term. We can use the box method, FOIL rule, or distributive property to confirm we have the right factorization. I'll use the distributive rule

(y+7)(y+8) = y(y+8) + 7(y+8)

(y+7)(y+8) = y^2 + 8y + 7y + 56

(y+7)(y+8) = y^2 + 15y + 56

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

i checked on edge

Answer: 5(x+3)(x-2)

Step-by-step explanation:

just read closely and pay attention in class.

Answer:

m∠D = 94°

Step-by-step explanation:

Quadrilateral ABCD is also called a cyclic quadrilateral or a quadrilateral that is inscribed in a circle.

Opposite angles in a cyclic Quadrilateral are supplementary, i.e the sum of two opposite angles in a Quadrilateral = 180°

m∠A + m∠C = 180°

m∠A = 74°

74° + m∠C = 180°

m∠C = 180° - 74°

m∠C = 106°

In a cyclic quadrilateral, the total sum of the angles outside the circle = 360°

i.e =

m∠AB + m∠BC + mDC + mAD = 360°

m∠DAB= ( m∠C) × 2

= 106° × 2 = 212°

m∠DAB = m∠AD + m∠AB

m∠AD = 79°

212° = 79° + m∠AB

m∠AB = 212° - 79°

= 133°

m∠ABC = m∠AB + m∠BC

m∠AB = 133°

m∠BC= 55°

m∠ABC = 133° + 55°

= 188°

We are asked to find m∠D

m∠D = 1/2m∠ABC

m∠ABC = 188°

m∠D = 1/2 × 188°

m∠D = 94°

Therefore, m∠D = 94°

v = 17 is your answer as an intergers or as a decimal rounded to the nearest tenth

Answer:

A third group in which no naps occur

Step-by-step explanation:

Control group: In a study or an experiment, the term "control group" is described as a specific group that doesn't receive or being provided any sort of treatment by the investigator or researcher ans therefore used as a particular benchmark or criteria to analyze or measure the way other tested participants do. It is generally used as a specific strategy that minimized the effects of different variable except independent variable.

Answer:

above is correect. i took the test.

Step-by-step explanation:

Answer:

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B

If Marguerite rents for 1 week, it will cost her the same at either company

h(x) = 5x - 5

Step-by-step explanation:

Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5

Answer: Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. In one week there are 7 days, therefore in x weeks the cost of rentals are given below:

For company A: f(x) = 15(7x)

For company B: g(x) = 100x + 5  

h(x) = f(x) – g(x) represents the difference between the two rate structures.

h(x) = f(x) - g(x) = 15(7x) - (100x + 5)

h(x) = 105x - 100x - 5

h(x) = 5x - 5

If Marguerite rents for 2 weeks:

The cost for company A = 15(7x) = 15(7 × 2) = $210

The cost for company B = 100x + 5 = 100(2) + 5 = 200 + 5 = $205

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B

If Marguerite rents for 1 weeks:

The cost for company A = 15(7x) = 15(7 × 1) = $105

The cost for company B = 100x + 5 = 100(1) + 5 = 100 + 5 = $105

If Marguerite rents for 1 week, it will cost her the same at either company

Answer:

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.

h(x) = 5x + 5

those are the answers on edge

Step-by-step explanation:

Answer:

12.6 units.

Step-by-step explanation:

According to cosine formula:

[tex]a^2=b^2+c^2-2bc\cos A[/tex]

Using cosine formula in triangle STU, we get

[tex](SU)^2=(ST)^2+(TU)^2-2(ST)(TU)\cos T[/tex]

[tex]t^2=(5)^2+(15)^2-2(5)(15)\cos (53^{\circ})[/tex]

[tex]t^2=25+225-150(0.60)[/tex]

[tex]t^2=160[/tex]

Taking square root on both sides.

[tex]t=\sqrt{160}[/tex]

[tex]t\approx 12.6[/tex]

Therefore, the value of t is 12.6 units.

Answer:

A. 7017

Step-by-step explanation:

common difference is 7

first term of the sequence is 24

by explicit formula a1 + ( n- 1)*d

24 + (1000-1)*7

24+999*7

24+6993

7017

Answer:

The correct option is;

B) The highest point of the mountain defined by the function is 16

Step-by-step explanation:

From the given information, we have;

The distance in feet from the edge of the mountain is given as the independent variable, x

The distance in feet from the ground (which is the height) is given the as the dependent variable f(x)

Therefore, given that the point (12, 16) are the values of x and f(x) such that x = 12 and f(x) = 16 and 16 is the largest value of f(x) in the data, therefore, 16 represents the highest defined point of the mountain.

Answer:

It's 22

Step-by-step explanation:

The height isn't important. The 2 opposite sides are always equal in a parallelogram.

Answer:

22

Step-by-step explanation:

The quadrilateral is a parallelogram.

A parallelogram has opposite sides equal.

x is equal to the length of the base.

x = 22

Answer:

Option d

Step-by-step explanation:

Continuous data are data that can take on any values within a range while discrete data can only take on particular values.

Thus for this case study, the number of police cars in different cities are usually not specific and may vary, thus this data is continuous.

Answer:

B. [tex]100 = 132.12sin2\theta[/tex]

Step-by-step explanation:

Given the horizontal distance in meters traveled by a projectile modeled by the function [tex]h = \frac{v_o^{2} }{4.9}sin\theta cos\theta[/tex]. If the initial velocity is 36 meters/second, the equation we would you use to find the angle needed to travel 100 meters is shown below;

[tex]h = \frac{v_o^{2} }{4.9}sin\theta cos\theta[/tex]

from trigonometry identity,

[tex]sin2\theta = 2sin\theta cos\theta\\sin\theta cos \theta = \frac{sin2\theta}{2}[/tex]

The equation will become;

[tex]h = \frac{v_o^{2} }{2*4.9}(sin2\theta)\\[/tex]

[tex]h = \frac{v_o^{2} }{2*4.9}sin2\theta[/tex]

Given h = 100 meters and v = 36 m/s

[tex]100 = \frac{36^{2} }{9.8}sin2\theta\\100*9.8 = 1296sin2\theta\\100 = \frac{1296}{9.8} sin2\theta\\100 = 132.12sin2\theta[/tex]

Answer:

132.12sin(2theta)=100

Step-by-step explanation:

Answer:

It could be 768 fl. oz I think?

Step-by-step explanation:

Bennett has 3 gallons of water and Jordan has 3 times as many gallons as bennett

Let's calculate how many gallons do Jordan has

Jordan has 9 gallons of water

every gallon of water contains 128 fluid ounces

Benett has 3 gallons

so  the fluid ounces are given by : 3*128=384

Benett has 384 ounces

Jordan has 9 gallons so 9*128 = 1152

so Jordan has 1152 fluid ounces

Answer:

Length of the square = 3 inches

Equation:   [tex]l = L - 3[/tex] and [tex]l = W - 1[/tex]

Step-by-step explanation:

Given

Area of the rectangle = 24

Required

Length of the square when the dimension of the rectangle is trimmed by 3 inches * 1 inches

Represent the dimension on the rectangle by L and W

Such that L represent Length and W, Width

This implies that

[tex]L * W = 24[/tex]

Represent the length of the rectangle by l

Such that

[tex]l = L - 3[/tex] and [tex]l = W - 1[/tex] (When trimmed)

Equate both expressions

[tex]L - 3 = W - 1[/tex]

Add 3 to both sides

[tex]L - 3 + 3 = W - 1 + 3[/tex]

[tex]L = W + 2[/tex]

Next is to list all possible dimensions of the rectangle;

[tex]Area(L,W) = Length * Width[/tex]

[tex]Area(24,1) = 24 * 1 = 24[/tex]

[tex]Area(12,2) = 12 * 2 = 24[/tex]

[tex]Area(8,3) = 8 * 3 = 24[/tex]

[tex]Area(6,4) = 6 * 4 = 24[/tex]

From the list above, the only calculation that fits our solution is

[tex]Area(6,4) = 6 * 4 = 24[/tex]

Such that

[tex]6 = 4 + 2[/tex]

By direct comparison of [tex]6 = 4 + 2[/tex] to [tex]L = W + 2[/tex];

[tex]L = 6[/tex]

[tex]W = 4[/tex]

Recall that

[tex]l = L - 3[/tex] and [tex]l = W - 1[/tex]

Substitute 6 for L and 4 for W

[tex]l = 6 - 3[/tex] and [tex]l = 4 - 1[/tex]

[tex]l = 3[/tex] in both cases

Hence, the length of the square is 3 inches

And the equation is  [tex]l = L - 3[/tex] and [tex]l = W - 1[/tex]

Answer:

Part 2:

The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points

The drawing of the angle cross section of a cylinder representing the banana is attached

Part 3:

When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle

The drawing of the perpendicular cross section of a cylinder representing the banana is

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

y>−5/4x+5

The y intercept is 5

The x intercept is

0 = -5/4x +5

-5 = -5/4x

-5 *-4/5 =- 5/4x *-4/5

4 =x

The x intercept is (4,0)

The line is dotted since there is no equals sign

We shade above the line

Answer:

First investment = $98000

Second = $413,000

Step-by-step explanation:

Given the following :

Investment 1:

Let first investment = f

Rate = 8% = 0.08

Investment 2:

$21,000 more than 4 times of investment 1:

4f + 21000

Rate = 10% = 0.1

Total annual interest earned from both :

$49,140

Interest on investment 1 + interest on investment 2 = $49,140

To solve:

Simple Interest = principal * rate * time

Time = 1 year

Total interest = (f * 0.08 * 1) + ((4f + 21000) * 0.1 * 1)

49140 = 0.08f + 0.4f + 2100

0.48f = 47040

f = 47040 / 0.48

f = 98000 = first investment

Second investment :

4f + 21000

= 4(98000) + 21000

= $413,000

Answer: -1.8

Step-by-step explanation:

Start at -5.5 and move the point on the number line up 3.7 spaces.

Hope it helps <3

Answer:

Your correct answer is -1.8

Step-by-step explanation:

−5.5 + 3.7

= −5.5+3.7

= −1.8

Answer:

Please use " ^ " for exponentiation: x^2 + 2x + 8 ≤ 0.

Let's solve this by completing the square:

x^2 + 2x + 8 ≤ 0 => x^2 + 2x + 1^2 - 1^2 + 8 ≤ 0. Continuing this rewrite:

(x + 1)^2 + 7 ≤ 0

Taking the sqrt of both sides: (x + 1)^2 = i*sqrt(7)

Then the solutions are x = -1 + i√7 and x = -1 - i√7

There's something really wrong here. I've graphed your function, x^2 + 2x + 8, and can see from the graph that there are no real roots, but only complex roots. Please double-check to ensure that you've copied down this problem correctly.

Answer:

B. The Empty Set

Step-by-step explanation:

Hope this helps!!! Have a great day!!!!   : )

Answer:

12 / 37 (or:=0.324324324...)

Step-by-step explanation:

Sinθ = opposite / hypotenuse

Hence

sinA = 12 / 37

(=0.324324324...)

Answer:

A = 19

Step-by-step explanation:

sin A = opp/hyp

sin A = 12/37

A = sin- ¹ 12/37

A=  18.92  or  19

Answer:

A 99% confidence level is saying that you are 99% positive that you null hypothesis will not be rejected. The critical value that comes with the confidence level is the Z-score. The Z-score can usually be found using the Z-score table found online. The Z-score for 99% confidence is 2.575. If they give you the Z-score and tell you to find it on a right tail graph you subtract the given z-score from alpha which is .5 and find what you got on the z-score table.

Ex: Given Z-score- 0.0079

.0079 - .5(alpha)=  0.4921.

The closest area to 0.4921 is 0.4922 at z = 2.42.

Hope this helps

Answer:

6π

Step-by-step explanation:

First we need to find the circumference of the circle. We know that the radius is 4 and the formula is πd or 2πr

Leaving it in terms of pi, the circumference is 8π

Now we need to find the length of the arc.

Since the missing part of the circle is labeled with a right angle, we know that it's exactly 1/4 of the whole circle. That means the arc we need to find is 3/4 of the circumference.

3/4 of 8π is 6π

Answer:

a) Vertex b) Maximum c) Axis of symmetry d) Linear e) x-intercept f) Parabola g) Minimum h) Quadratic i) Down

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

d) The first difference of a quadratic sequence will be a linear sequence.

h) The second difference of a quadratic will be constant.

i) image attached

Answer:  f(x) is an odd function

Step-by-step explanation:  The major characteristic of odd functions is that one end of the graph goes down to negative infinity, the other end goes up to positive infinity.

Answer:

f(x) is an odd function.

Step-by-step explanation:

Answer:

-\frac{7}{6}

Step-by-step explanation:

We can use the slope formula for the segment that joins any two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]:

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

which in our case gives:

[tex]slope=\frac{y_2-y_1}{x_2-x_1} = \frac{-2-5}{3-(-3)}=\frac{-7}{6} =-\frac{7}{6}[/tex]

Answer:

C.  3

Step-by-step explanation:

Perpendicular lines have slopes that are negative inverses of the other.

This inverse of -1/3 is -3.  The negative of -3 is 3.

The slope of the perpendicular line is 3.

Answer:

Surface Area: 150.796

Volume: 141.372

Step-by-step explanation:

Cylinder Surface Area: 2Πrh+2Πr^2

r=3

h=5

2Π15+2Π9=30Π+18Π=48Π=150.796

Volume: Πr^2h

Π45=141.372

Hope this helps! BRAINLIEST would really help me:)

Answer:

150.8 units²

141.37 units³

Step-by-step explanation:

Surface area of cylinder:

[tex]2 \pi r^2+2 \pi rh[/tex]

[tex]r=3\\h=5[/tex]

[tex]2 \pi (3)^2+2 \pi (3)(5)[/tex]

[tex]18\pi +30\pi[/tex]

[tex]=150.8[/tex]

Volume of the cylinder:

[tex]\pi r^2 h[/tex]

[tex]r=3\\h=5[/tex]

[tex]\pi (3)^2 (5)[/tex]

[tex]45\pi[/tex]

[tex]=141.37[/tex]