how many solutions does y = x^2 + 7x - 11 have?

The standard form of the equation of the parabola is y + 3 = (1/3) · (x - 3)² and The factored form of the equation of the parabola is y = (1/3) · x · (x - 6).

Mathematically speaking, parabolae are defined by second order polynomials. The standard form of the equation of the parabola is defined by:

y - k = C · (x - h)²     (1)

Where C is the vertex constant.

And the factored form has this form:

y = k · (x - r₁) · (x - r₂)     (2)

First, we determine the standard form of the equation of the parabola: (h, k) = (3, - 3) and (x, y) = (0, 0)

0 - (- 3) = C · (0 - 3)²

3 = 9 · C

C = 1/3

Then, the standard form of the equation of the parabola is y + 3 = (1/3) · (x - 3)². Now we proceed to determine the factored form of the parabola: (r₁ = 0, r₂ = 6), (h, k) = (3, - 3)

- 3 = k · (3 - 0) · (3 - 6)

- 3 = k · 3 · (- 3)

- 3 = - 9 · k

k = 1/3

The factored form of the equation of the parabola is y = (1/3) · x · (x - 6).

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Answer:

tanΘ = [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{5}{12}[/tex]

Answer:

Step-by-step explanation:

The surface area of a square pyramid is 1/2 the product of its base perimeter & slant height.

SA = area of base + 1/2 (perimeter of base * slant height)

So, we can substitute 12 and 10 into this equation.

The area of the base is 12*12 (144). The perimeter of the base is 48mm.

144 + 1/2(48*10) = Surface Area.

144 + 240 = Surface Area.

384mm = Surface Area.

Hope that helps :)

Answer:

4

Step-by-step explanation:

to find the x intercept of a line in standard form we can simply set y as 0 and find x

4x - 7(0) = 16

4x = 16

x = 4

the answer is 4

Answer: [tex]68^{\circ}[/tex]

Step-by-step explanation:

Assuming AC is a tangent, this means [tex]m\angle BAC=90^{\circ}[/tex].

Since arc BY measures 44 degrees, by the inscribed angle theorem, [tex]m\angle BAY=22^{\circ}[/tex].

This means [tex]m\angle YAC=90^{\circ}-22^{\circ}=68^{\circ}[/tex]

Answer:

yes

Step-by-step explanation:

every hours of training has mapped to monthly pays and each element in hour of training has mapped to unique element in monthly pay.

Answer:

y = -5/4x +1

Step-by-step explanation:

The slope-intercept form of a line is given by

y = mx + b  where m is the slope and b is the y intercept

We are given the slope and a point on the line

y = -5/4 x + b

We can substitute the point for x and y and solve for b

-9 = -5/4(8)+b

-9 = -10+b

Add 10 to each side

-9+10=-10+10+b

1 = b

The slope intercept form of the equation is

y = -5/4x +1

This lane symbol is used for marking the beginning and ending of a left turn to the drivers.

What are lane symbols?

A permitted lane usage is denoted by a lane symbol. For example, a lane marked with a diamond is one that is designated for high-occupancy cars.  A lane symbol of a bicycle marks that the lane is designated for cyclists. At crossings, arrows indicate movements that are necessary or allowed. The user of the roadway must yield when there is a row of solid triangles. Likewise, two large curved arrows facing each other on a lane in the middle of a two way road with dashed lines on either sides indicate the beginning and ending of a left turn.

A Lane symbol or marking are also utilized to warn drivers of potentially dangerous situations that may be coming up. For instance, a triangle with no filling indicates a yield ahead. A speed hump is indicated by a succession of lines across a lane that get bigger and wider.

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The linear equation for the graph in terms of x is given by: y = -0.5x - 3.

A linear function is modeled by:

y = mx + b

In which:

Looking at the graph, when x = 0, y = -3, hence the y-intercept is of b = -3. The graph also passes through point (2,-4), hence the slope is given by:

m = (-4 - (-3))/(2 - 0) = -1/2 = -0.5.

Hence the equation is:

y = -0.5x - 3.

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The negative of the expression -2y+13 is 2y-13.

Given Expression:-2y+13

We know that an expression is a combination of numbers, variables, symbols, indeterminants, etc. It is not expressed in equal to form. It expresses a relationship but we cannot find the value of variable because it is usually not present in equal to form.

We have to find the negative of the expression -2y+13 and to find out that we need to just put a negative mark in front of the expression and then adjust the expression for finding the negative of that expression.

Negative of -2y+13=-(-2y+13)

=2y-13.

Negative of an expression expresses opposite thing.

Hence the negative  of -2y+13 is 2y-13.

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Answer:

b = 12

Step-by-step explanation:

since a² + b² = c²

we can find b by pythagorean theorem.

sqrt(13² - 5²) = b

hence,

b = 12

Answer:   12

Step-by-step explanation:

To find a length of a right triangle, we can use Pythagorean theory:

            leg² + leg² = hypotenuse²              

                  5² + b² = 13²

                 25 + b² = 169

                          b² = 144

                            b = [tex]\sqrt{144}[/tex]

                             b = 12

The total salary juma receives for the month of July before the deductions is sh. 12,800

Let

School fees + farming = 1/2x + 1/8x

= 4x+x/8

= 5/8x

Amount remaining = x - 5/8x

=8x-5x /8

= 3/8x

Amount spent on food = 2/3 × 3/8x

= 6/24x

= 1/4x

So,

1/4x = sh.3200

x = 3200 ÷ 1/4

x = 3200 × 4

x = sh. 12,800

Complete question:

Juma spent half of his salary on school fees one-eighth on farming and two thirds of the reminder on food . Calculate his July salary if he spent sh.3200 on food

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Answer:

1056.24 cm^3

Step-by-step explanation:

The volume of a cylinder is [tex]\pi r^2h[/tex]. The problem says to use [tex]\pi[/tex]=3.14

Plug in your numbers [tex]3.14*4.8^2*14.6=1056.24[/tex]

Based on the coordinates given, the location that is being described is Cook Inlet, in the Gulf of Alaska.

The coordinates of 61°N, 150°W means that the place is located in the Northern and Eastern hemisphere.

When a map is used, it points to an area in the Gulf of Alaska that is very close to the Cook Inlet which is close to Anchorage.

Question is:

Determine what country or place is located on the given approximate coordinates.

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Answer:

[tex]f(x)=2(2)^{0.5x}-3[/tex]

Step-by-step explanation:

Parent function:

[tex]g(x)=2^x[/tex]

Properties of the given parent function:

Given form of function f(x):

[tex]f(x)=a(b)^{kx}+c[/tex]

If the parent function is  [tex]g(x)=2^x[/tex]  then  b = 2:

[tex]\implies f(x)=a(2)^{kx}+c[/tex]

From inspection of the graphed function f(x):

Therefore, the y-intercept has shifted 2 units down, yet the asymptote has shifted 3 units down.  This implies that there has been a vertical shift of 3 units down and a vertical stretch.

The vertical shift is denoted by the variable "c" so c = -3:

[tex]\implies f(x)=a(2)^{kx}-3[/tex]

The vertical stretch is denoted by the variable "a".  To find value of a, substitute the point of the y-intercept into the equation:

[tex]\begin{aligned}f(0) & = -1\\\implies a(2)^{k \times 0}-3 & =-1\\a-3 & = -1\\a-3+3 & = -1+3\\a & = 2\end{aligned}[/tex]

Therefore, as a = 2:

[tex]\implies f(x)=2(2)^{kx}-3[/tex]

From inspection of the given graph, the curve passes through point (4, 5).  Substitute this point into the equation to find the value of k:

[tex]\begin{aligned}f(4) & = 5\\\implies 2(2)^{4k}-3 & =5\\2(2)^{4k}& =8\\(2)^{4k}& =4\\(2)^{4k}& =2^2\\4k & = 2\\k & = 0.5\end{aligned}[/tex]

Therefore, the equation of the function f(x) is:

[tex]\implies f(x)=2(2)^{0.5x}-3[/tex]

1. x = a

2. y = b

3. A vertical line has an undefined slope.

4. rise/run or Change in y/change in x (m) = y2 - y1 / x2 - x1

5. Rewrite the equation in slope-intercept form to determine the y-intercept.

In slope-intercept form, the equation of a line in slope-intercept form is, y = mx + b, where m is the slope and the y-intercept = b.

1. The slope of a vertical line is undefined, therefore, the equation for a vertical line is given as: x = a, where a is the value of the x-intercept.

A vertical line that contains (a, b) will have the equation, x = a.

2. The slope of a horizontal line is 0, therefore, the equation of the horizontal line is, y = b, where b is the y-intercept.

A horizontal line that contains (a, b) will therefore have the equation, y = b.

3. A vertical line has an undefined slope.

4. For example, if we have the two points (3, 3) and (0, 5), two methods to find the slope are:

rise/run

or

Change in y/change in x (m) = y2 - y1 / x2 - x1 = 5 - 3 / 0 - 3 = 2/-3 = -2/3.

5. If we have an equation in point-slope form, for example, y - 3 = 2(x - 4), to find the coordinates of its y-intercept, rewrite the equation in slope-intercept form to determine the y-intercept:

y - 3 = 2x - 8

y = 2x - 8 + 3

y = 2x - 5

The y-intercept is -5, thus, the coordinates would be: (0, -5).

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The mistakes that Joan made are:

A bar chart is a graph that shows the numerical values of variables represented by the height rectangles of equal width.

In a bar graph, the rectangles must be of equal width and the space between each bars must be equal.

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Step-by-step explanation:

JKL is congruent to ABC

side LK corresponds to WV and CB

angle JLK corresponds to angle UWV and angle ACB

Answer:

2 layers, 3×2 cans per layer

Step-by-step explanation:

Factors of 12: 1, 2, 3, 4, 6, 12

The box can have 1 layer of 12 cans, 2 layers of 6 cans each, or 3 layers of 4 cans each.

In each case below, the total surface area is 2(LW + LH + WH)

1 layer, 12×1 cans

L = 84 cm; W = 7 cm; H = 10 cm

SA = 2996 cm²

1 layer, 6×2 cans

L = 42 cm; W = 14 cm; H = 10 cm

SA = 2248 cm²

1 layer, 4×3 cans

L = 28 cm; W = 21 cm; H = 10 cm

SA = 2156 cm²

2 layers, 6×1 cans per layer

L = 42 cm; W = 7 cm; H = 20 cm

SA = 2548 cm²

2 layers, 3×2 cans per layer

L = 21 cm; W = 14 cm; H = 20 cm

SA = 1988 cm²          <--------------- smallest surface area

3 layer, 4×1 cans per layer

L = 28 cm; W = 7 cm; H = 30 cm

SA = 2492 cm²

3 layers, 2×2 cans per layer

L = 14 cm; W = 14 cm; H = 30 cm

SA = 2072 cm²

Answer:

500 is your answer.

Step-by-step explanation:

First solve the length of side BC, CD, EF and FA   Since BC = CD = sqrt( 10^2 + 10^2) BC = CD = 14.1421  

FA = EF = sqrt(10^2 + 20^2) = 23.3607  

So the perimeter = 10 + 10 + 14.1421 + 14.1421 + 23.3607 = 93

The area is made up be triangle FAE, rectangle ABDE and triangle BCD

A = 0.5(20)(20) + (10)(20) + 0.5(20)(10)

A = 500 sq units

Answer: 2,464 boxes are made in 7 days.

Step-by-step explanation:

1 day = 352 boxes

7 days = ?

To solve this word problem, you can multiply 352 and 7.

352*7= 2464

Answer:

E) 200

Step-by-step explanation:

Let the length of the side after cutting the corners =x cm

Length of the side before cutting the corners = x + 4 cm

Area of square before cutting =  (x + 4)² square cm

Area of that square that was cut  = 2*2 = 4 cm²

Area of 4 squares cut from all 4 corners = 4 * 4 = 16 cm²

Area of internal surface area = 180 square cm

                       (x + 4)² -  4*4        = 180

                   x² + 2*4*x + 4² - 16 = 180

 {expand using the identity  (a + b)² = a² + 2ab + b²) }

                     x²  + 8x + 16 -16   = 180

                        x² + 8x  - 180    = 0

                  x² + 18x - 10x - 180 = 0

               x( x + 18) - 10(x + 18) = 0

                         (x + 18) (x - 10) = 0

  x - 10 = 0   {Ignore x +18 = 0}

         x = 10

           length =  x = 10 cm

          breadth = x = 10 cm

         height  = 2 cm

Volume of open box = length * breadth * height

                                  = 10 * 10 * 2

                                  = 200 cm³

Answer:

a)  u - v

b)  2v - 2

c)  3u + 3

d)  ¹/₂

Step-by-step explanation:

Given:

 [tex]u=\log_{10}3[/tex]

 [tex]v=\log_{10}5[/tex]

Part (a)

Rewrite 0.6 as a fraction:

[tex]\implies \log_{10}(0.6)=\log_{10}\left(\dfrac{3}{5}\right)[/tex]

[tex]\textsf{Apply the quotient log law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay:[/tex]

[tex]\implies \log_{10}\left(\dfrac{3}{5}\right)=\log_{10}3-\log_{10}5[/tex]

Substitute the values of u and v:

[tex]\implies \log_{10}3-\log_{10}5=u-v[/tex]

Part (b)

Rewrite 0.25 as 25/100:

[tex]\implies \log_{10}(0.25)=\log_{10}\left(\dfrac{25}{100}\right)[/tex]

[tex]\textsf{Apply the quotient log law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay[/tex]

[tex]\implies \log_{10}\left(\dfrac{25}{100}\right)=\log_{10}(25)-\log_{10}(100)[/tex]

Rewrite 25 as 5² and 100 as 10²:

[tex]\implies \log_{10}(25)-\log_{10}(100)=\log_{10}(5^2)-\log_{10}(10^2)[/tex]

[tex]\textsf{Appy the Power log law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \log_{10}(5^2)-\log_{10}(10^2)=2\log_{10}5-2\log_{10}10[/tex]

[tex]\textsf{Apply the log law}: \quad \log_aa=1[/tex]

[tex]\implies 2\log_{10}5-2\log_{10}10=2\log_{10}5-2(1)[/tex]

Substitute the value of v:

[tex]\implies 2\log_{10}5-2(1)=2v-2[/tex]

Part (c)

Rewrite 27000 as 30³:

[tex]\implies \log_{10}(27000)=\log_{10}(30^3)[/tex]

[tex]\textsf{Appy the Power log law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \log_{10}(30^3)=3\log_{10}(30)[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies 3\log_{10}(30)=3\log_{10}(3)+3\log_{10}(10)[/tex]

[tex]\textsf{Apply the log law}: \quad \log_aa=1[/tex]

[tex]\implies 3\log_{10}(3)+3\log_{10}(10)=3\log_{10}(3)+3(1)[/tex]

Substitute the value of u:

[tex]\implies 3\log_{10}(3)+3(1)=3u+3[/tex]

Part (d)

Rewrite √10 as [tex]10^{\frac{1}{2}}[/tex] :

[tex]\implies \log_{10}(\sqrt{10})=\log_{10}(10^{\frac{1}{2}})[/tex]

[tex]\textsf{Appy the Power log law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \log_{10}(10^{\frac{1}{2}})=\dfrac{1}{2}\log_{10}(10)[/tex]

[tex]\textsf{Apply the log law}: \quad \log_aa=1[/tex]

[tex]\implies \dfrac{1}{2}\log_{10}(10)=\dfrac{1}{2}(1)=\dfrac{1}{2}[/tex]

The is an observational study.

What is  an observational study?

In an observational study, researchers examine the effects of a particular intervention, risk, diagnostic test, or treatment without trying to control who is exposed to it.

By having a control group, or those who are not exposed, and an experimental group, or those who are subjected to the intervention, treatment, etc., an observational study contrasts from an experimental research, where the scientists are controlling who gets exposed to the treatment, intervention, etc. The groups are randomly assigned or picked in the best studies.

Reason Behind it Being an Observational Study

Since, in this case also, the two categories of men and women, the candidates are randomly picked for the survey of the new software programmer feature. Hence, it is a scenario of observational study.

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Answer:

To solve this, we need to first evaluate the given expression. We can do that by simplifying the contents of each bracket, starting with the innermost one:

[4-5{1-(4-3+1)}]

⇒ [4 - 5{1 - (2)}]

⇒ [4 - 5{-1}]

⇒ 4 - (-5)

⇒ 4 + 5

⇒ 9

Now we can calculate what 9 out of 100 is:

9 of 100  =  [tex]\frac{9}{100}[/tex]

              ⇒  9%

The length of the board is 0.665 meters wide. When the boarder is added in all 4 edges, the length decrease by 0.05 meters on both side. So, the remaining length across is 0.665 - 0.5 x 2 = 0.565, so b.

*but maybe it's not a rectangle*

Answer:

See below

Step-by-step explanation:

2^3    is   two cubed     ...now multiply times 7

7 * 2^3    

Answer:

Step-by-step explanation:

There are two different relations here that can be used to write equations for the value of x:

Using the angle relation, we have ...

  ∠CMA ≅ ∠BMA

  (9x)° = 90°

  x = 90/9 = 10

Using the found value of x in the expressions for the segment lengths, we find ...

  MB = 2x -4 = 2(10) -4 = 16

  CM = x +6 = 10 +6 = 16 . . . . . . . congruent to MB, as it should be

  CB = CM +MB = 16 +16 = 32