-. If the expression (x-7) was placed in ax? +bx+c form, which of the following would be
the value of b?
(1) -7
(3) -14
(2) 7
(4) -49
PLEASE HELP

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[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]

➡[tex]\:4a + 1 = a + 7[/tex]

Combining like terms, we have

➡[tex]\:4a - a = 7 - 1[/tex]

➡[tex]\:3a = 6[/tex]

➡[tex]\:a = \frac{6}{3} [/tex]

➡[tex]\:a = 2[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

➪ [tex] \: 4 \times 2 + 1 = 2 + 7[/tex]

➪ [tex] \: 8 + 1 = 9[/tex]

➪ [tex] \: 9 = 9[/tex]

➪ [tex] \: L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]

Answer:

x = 4

Step-by-step explanation:

The line in the triangle is an angle bisector and divides the opposite sides into segments that are proportional to the other 2 sides, that is

[tex]\frac{x+6}{20}[/tex] = [tex]\frac{x}{8}[/tex] ( cross- multiply )

20x = 8(x + 6) = 8x + 48 ( subtract 8x from both sides )

12x = 48 ( divide both sides by 12 )

x = 4

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

Explanation:

We use the cosine ratio here. Make sure your calculator is in degree mode.

cos(angle) = adjacent/hypotenuse

cos(69) = x/10

10*cos(69) = x

x = 10*cos(69)

x = 3.583679495453 which is approximate

x = 3.6

Answer: The ASAP Math program provides an opportunity for additional small group instruction for students who find the math program challenging. Students in grades 1 to 4 will come to the ASAP room two to three times a week during the math block.

Answer:

True

Step-by-step explanation:

Smoking damages your entire cardiovascular system. Speaking of this Nicotine causes blood vessels to tighten, which restricts the flow of blood. Over time, the ongoing narrowing, along with damage to the blood vessels, can cause *peripheral artery disease*. Smoking also raises blood pressure, weakens blood vessel walls, and increases blood clots.

* Peripheral artery disease is a common circulatory problem in which narrowed arteries reduce blood flow to your limbs

Hope this helps :) Brainliest would be appreciated XD

Answer:

4.5 feet

Step-by-step explanation:

Line AB || Line CD {sun height are parallel}

Angle ACB parallel to Angle DEC = 90°

Triangle ABC is parallel to Triangle DCE

12/61 * 2.5

=4.5 feet

Answer:

1/2

Step-by-step explanation:

2, 3, and 5 are the prime numbers. Therefore, it would be 3/6 or 1/2 chance she rolls a prime number.

Answer:

$14.7

Step-by-step explanation:

Zeke owns stock in a high tech firm

Each share is valued at $21

It's is 30% less than the amount it was purchased

Therefore Zeke pay per share can be calculated as follows

= 21× 30/100

= 21×0.3

= 6.3

= 21-6.3

= 14.7

Hence Zeke's pay per share is $14.7

Given:

A figure of a rectangular prism with length l, width w and height h.

To find:

The surface area of the rectangular prism.

Solution:

The product of twice of the length l and the width w is:

[tex]2\times l\times w=2lw[/tex]          ...(i)

The product of twice of the length l and the height is:

[tex]2\times l\times h=2lh[/tex]           ...(ii)

The product of twice of the width w and the height h is:

[tex]2\times w\times h=2wh[/tex]       ...(iii)

The surface area of the prism is the sum of (i), (ii) and (iii). So, the expression for the surface area is:

[tex]A=2lw+2lh+2wh[/tex]

[tex]A=2(lw+lh+wh)[/tex]

Therefore, the required expression is [tex]2(lw+lh+wh)[/tex].

The set {1, 2, 3} has 8 subsets.

A set with 'n' elements in it can have 2n subsets.

Answer:

- 2/5

Step-by-step explanation:

(3/5 + 1/5) + (4/5 - 2/5) = 6/5

6/5 - (9/5-1/5) = - 2 /5

Answer:

HCF = 1

Step-by-step explanation:

Smallest 2 digit composite number = 10

Smallest  3 digit prime number = 101

Factors of 10 = 1 , 2 , 5

Factors of 101 = 1 , 101

HCF = 1

Answer:

Step-by-step explanation:

The distance between the vertex and the directrix is 4 units, that means that p = 4 in the equation

[tex](y-k)^2=4p(x-h)[/tex] and h and k are the coordinates of the vertex. Filling in:

[tex](y+4)^2=4(4)(x+2)[/tex] which simplifies to

[tex](y+4)^2=16(x+2)[/tex] choice C

Option C is correct, (y+4)² = 16(x+2) is the the equation of the parabola, in vertex form, with vertex at (-2,-4) and directrix x = -6

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

The focus of the parabola is at a point that is equidistant to the vertex and the directrix.

Since the directrix is x = -6, the focus is at (-2+4,-4) = (2,-4).

The vertex form of the equation of a parabola is given by:

(y - k)² = 4p(x - h)

where (h, k) is the vertex and p is the distance between the vertex and focus.

In this case, (h, k) = (-2,-4) and the focus is at (2,-4). Therefore, p = 4.

Substituting the values into the vertex form equation, we get:

(y + 4)² = 4(4)(x + 2)

Simplifying, we get:

(y + 4)² = 16(x + 2)

Hence, (y+4)² = 16(x+2) is the the equation of the parabola, in vertex form, with vertex at (-2,-4) and directrix x = -6

To learn more on Parabola click:

https://brainly.com/question/31142122

#SPJ5

Answer:

✓✓ Area of traingle = 1.2 cm^2 ✓✓

Step-by-step explanation:

Hello mate (◕ᴗ◕✿)

=>> In above traingle, height and hypotenuse are given

=> height = 12 cm

=> Hypotenuse = 14 cm

✓✓ Area of traingle = 1/2(base*height) ✓✓

we need to find base of above traingle

Base = √Hypotenus - √Perpindicular

Base = √14 - √12

Base = 3.7 - 3.4

Base = 0.2 cm

Now, we can find area of traingle

Area of traingle = 1/2(Base*Height)

Area of traingle = 1/2(0.2*12)

Area of traingle = 6*0.2

Area of traingle = 1.2 cm^2

Hope it helps you mate (. ❛ ᴗ ❛.)

Answer :

➢ 43.3 cm²

Explanation :

let the missing side be c

a = 12 cm

b = 14 cm

Pythagoras theorem :

➢ a² + c² = b²

➢ 12² + c² = 14²

➢ 144 + c² = 196

➢ c² = 196 - 144

➢ c² = 52

➢ c = √52

➢ c = 7.21

Area = 1/2 × a × c

➢ 1/2 × 12 × 7.21

➢ 6 × 7.21

➢ 43.26 cm²

➢ 43.3 cm² [ round off to 1 decimal place ]

Answer:

Distribute 1.2 to 6.3 and -7x

Combine 3.5 and 7.56

suhtract 11.06 from both sides

Answer: 360 is a complete circle meaning the figure will be back where it was originally

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the roots of a quadratic equation, you need to solve the quadratic equation by using the quadratic formula.

OR

You can use the (Equation/Function) mode on the calculator.

[tex]\frac{-b+-\sqrt{b^{2} -4ac } }{2a} x \neq 0[/tex]

For this equation,

a = 3

b = 15

c = -5

X1 = [tex]\frac{-15+\sqrt{15^{2} -4(3)(-5) } }{2(3)} x \neq 0[/tex]

X2 = [tex]\frac{-15-\sqrt{15^{2} -4(3)(-5) } }{2(3)} x \neq 0[/tex]

Solving this on the calculator and you should get

X1 = [tex]\frac{=15+\sqrt{285} }{6}[/tex] X2 = [tex]\frac{=15-\sqrt{285} }{6}[/tex]

a, b, c = constants, where a ≠ 0

x  = the unknown

Answer:

yes

Step-by-step explanation:

both angels are the same and that means that the length of the parallel sides are also the same

Answer:

D

Step-by-step explanation:

Have a great summer :)

Answer:

C

Step-by-step explanation:

The slope is negative, so we can exclude the graph A and D

If we substitute y with 2 and x with -3 we have

2 = -4/3 (-3) -2

2 = 4 - 2

2 = 2

the equality is verified so C is the answer

Answer:

20 apples, 32 pears

Step-by-step explanation:

Using a for number of apples and p for number of pears, you get a+p=52 (amount) and 0.4a+0.5p=24 (cost).

One way of solving simultaneous equations is using like terms and adding/subtracting them to remove a variable. There aren't any like terms here, but we can create some by multiplying terms.

Multiplying the second equation by 2 gives 0.8a+p=48, so that makes a like term.

Since the symbols are the same in front of the like term, we subtract the second term from the first one. This gives 0.2a=4.

Dividing by 0.2 gives a=20.

We can sub this into either equation to get the value of p.

a+p=52, so 20+p=52, meaning p=32.

**This content involves simultaneous equations, which you may want to revise. I'm always happy to help!

Answer:

Step-by-step explanation:

r=x(a+b)/x

r/x=a+b-b

r/x-b=a

Answer:

[tex]Q_3 = 64[/tex]

Step-by-step explanation:

Given

Box of a box plot with the range: 60 - 64

Required

The upper quartile

To do this, we simply identify the endpoint of the range

Given that the range of the box is 60 to 64.

We have:

[tex]Start = 60[/tex]

[tex]End = 64[/tex]

Hence:

[tex]Q_3 = 64[/tex]

Answer:

the 9th term would be  -15

Step-by-step explanation:

Answer:

21.8

Step-by-step explanation:

87.2 divided by 4

Answer:

261.60

Step-by-step explanation:

its 3 times 87.20

OPTION B is the correct answer.

Hope it helps you...

Answer:

option B

Step-by-step explanation:

[tex]4^{\frac{2}{5} } *4^{\frac{-2}{5} }[/tex]

in multiplication if base are same u can add their power (exponent)

[tex]4^{\frac{2}{5} + \frac{-2}{5} } \\[/tex]

here since the denominator of the fraction in exponent are same u can add or subtract their numerator.

[tex]4^{\frac{2-2}{5} } \\4^{\frac{0}{5} } \\4^{0} \\1[/tex]

note: any base with the power 0 is always considered as one.

Answer:

5

Step-by-step explanation:

The highest power is 5 so the degree of the monomial is also 5.

Answer:

The answer is C≈49.64

Answer:

C=2πr=2·π·7.9≈49.63716

Step-by-step explanation:

brainliest??

Answer:

7.5 minutes

Step-by-step explanation:

Given

See attachment for complete question

Let

[tex]t \to time[/tex]

[tex]y \to capacity[/tex]

From the question, we have the following points

[tex](t_1,y_1) = (0,7)[/tex] --- When he first sees it

[tex](t_2,y_2) = (3,5)[/tex] --- 3 minutes later

First, we calculate the rate (m)

[tex]m = \frac{y_2 -y_1}{t_2 -t_1}[/tex]

[tex]m = \frac{5 -7}{3 -0}[/tex]

[tex]m = -\frac{2}{3}[/tex]

The discharge rate is 2/3 gallons per minute

To calculate the additional minute, we simply consider the capacity of the tank at the later time. i.e. 5 gallons

To calculate time (t), we have:

[tex]Rate * Time = Capacity[/tex]

[tex]\frac{2}{3} * t = 5[/tex]

Solve for t

[tex]t = 5 *\frac{3}{2}[/tex]

[tex]t = \frac{15}{2}[/tex]

[tex]t = 7.5[/tex]

Answer:

length- 10cm, width- 5cm

Step-by-step explanation:

You want to convert this into an algebraic equation.

Since a=lw, in this case, 50=lw. Subbing (x+3) for l and (x-2) for w, we get the equation (x+3)(x-2)=50.

Using FOIL, we can expand the brackets to make x²-2x+3x-6=50 and collect like terms to x²+x-6=50.

We want all the numbers on one side (to use the null factor law), so we subtract 50 from both sides. This gives x²+x-56=0.

From there, we factorise it, which becomes (x-7)(x+8)=0. (I used the cross method for this)

With the null factor law, one of the brackets must be equal to 0, meaning x-7=0 or x+8=0. This gives x as either 7 or -8.

With measurement, units must be positive, meaning it has to be 7. We can sub this for x in the 2 equations (length and width) to get the answers.

Length=x+3 becomes 7+3, which is 10cm.

Width=x-2 becomes 7-2, which is 5cm.

**This content involves writing, expanding, and factorising quadratic equations, and the null factor law which you may wish to revise. I'm always happy to help!