Find all real solutions of the equation: x 2 + 3x − 10 = 0

9514 1404 393

Answer:

Step-by-step explanation:

The midpoint divides the segment into two equal lengths:

  AB = BC

  5x -2 = 9x -10

  8 = 4x

  2 = x

  AB = 5(2) -2 = 8

  AC = 2AB = 2(8) = 16

Answer:

k = -2

Step-by-step explanation:

83=4k-7(1+7k)

Distribute

83=4k-7-49k

Combine like terms

83 = -45k -7

Add 7 to each side

83+7 = -45k-7+7

90 = -45k

Divide each side by -45

90/-45 = -45k/-45

-2 = k

Answer:

Step-by-step explanation:

Step 1: Use 7 to open the bracket :

-7(1+7k)=-7-49k

Step 2: Collect like terms

Step 3 : Divide both sides of the equation by -45

[tex]83=4k-7(1+7k) \\ \\83 = 4k-7-49k\\\\ 83+7=4k-49k\\\\90 = -45k\\\\\frac{90}{-45} = \frac{-45k}{-45} \\\\k = -2[/tex]

Answer:

29 losses in 49 games.

Step-by-step explanation:

The number of games that they lost in the first 12 = 12 - 5 = 7

7/12 = x / 49           Multiply both sides by 49

7*49 / 12 = x

x = 343/12

x = 28.5833

What do you do with the 0.5833? I would say round up to 29.

Answer:

345/5=69

Step-by-step explanation:

345/5=69

355/5=71

It's given that the Bracelet uses 3 times the number of beads that's used in making a single earring.

It's also given that one single earing has 13 beads. So a single bracelet would have (3×13) beads .... and that's equal to 39.

Making a single set of jewellery needs a pair of earrings and a Bracelet.

So total number of required beads will be =

Answer:

Using a graphing calc.

Step-by-step explanation:

Answer: 33% is moisture content

Step-by-step explanation:

120kg - 80kg = 40kg

40 of 120 is %

Work:

40/120 = 0.33

0.33x100

= 33%

Answer:

Option B, x ≈ -2.25

Step-by-step explanation:

3^x-2=(x-1)/(x^2+x-1)

or x ≈ -2.21166

so it's closest to the answer of the 2nd option

Hence the area of the second rhombus is 45 square meters

The area of a rhombus is expressed as

A = base * height

For the rhombus with an area of 5 square meters and a side length of 3 meters

Height = Area/length

Height = 5/3 metres

Since the length of a similar rhombus is 9meters, the scale factor will be expressed as;

k = ratio of the lengths = 9/3

k = 3

Height of the second rhombus = 3 * height of the first rhombus

Height of the second rhombus = 3 * 5/3

Height of the second rhombus = 5 meters

Area of the second rhombus = length * height

Area of the second rhombus = 5 * 9

Area of the second rhombus = 45 square meters

Hence the area of the second rhombus is 45 square meters

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The correct option is option B;

(B) 45 square meters

The known parameters in the question are;

The area of the rhombus, A₁ = 5 m²

The length of one of the sides of the rhombus, a = 3 m

The length of a side in a similar rhombus, b = 9 m

The unknown parameter;

The area of the second rhombus

Strategy or method;

We have that two shapes are similar if their corresponding sides are proportional

From the above statement we get that the ratio of the areas of the two shapes is equal to the square of the ratio of the lengths of the corresponding sides of the two shapes of follows;

[tex]\begin{array}{ccc}Length \ Ratio&&Area \ Ratio\\\dfrac{a}{b} &&\left (\dfrac{a}{b} \right)^2 \\&&\end{array}[/tex]

Let the area of the second rhombus be A₂, we get;

[tex]Area \ ratio = \dfrac{A_1}{A_2} = \left( \dfrac{a}{b} \right)^2[/tex]

Where;

a = 3 m, b = 9 m, and A₁ = 5 m², we get;

[tex]Area \ ratio = \dfrac{5 \ m^2}{A_2} = \left( \dfrac{3 \, m}{9 \, m} \right)^2 = \dfrac{1}{9}[/tex]

Therefore;

9 × 5 m² = A₂ × 1

A₂ = 45 m²

The area of the second rhombus, A₂ = 5 m².

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Answer:

Hello,

What is tan 30°?

[tex]tan(30^o)=\dfrac {\sqrt{3} }{3}[/tex]

Step-by-step explanation:

[tex]sin(30^o)=\dfrac{1}{2} \\\\cos(30^o)=\dfrac{\sqrt{3} }{2} \\\\\\tan(30^o)=\dfrac{sin(30^o)}{cos(30^o)} \\tan(30^o)=\dfrac{\dfrac{1}{2} } { \dfrac{\sqrt{3} }{2} }\\\\ =\dfrac {1*2}{2*\sqrt{3} }\\\\ =\dfrac {\sqrt{3} }{3}[/tex]

The value of tan 30° is 1/√3

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.

Tan 30° = sin 30° / cos 30°

We know that, sin 30° = 1/2

cos 30° = √3/2

Therefore,

Tan 30° = 1/2 ÷ √3/2

Tan 30° = 1/2 x 2/√3

Tan 30° = 1/√3

Hence, the value of tan 30° is 1/√3

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Answer:

see similar to the number of the number

Answer:

c=18

Step-by-step explanation:

5/30=3/c

1/6=3/18

1✖️3=3

6✖️3=18

Step-by-step explanation:

Recognize the relation between the graph and the slope–intercept form of an equation of a line

Identify the slope and y-intercept form of an equation of a line

Graph a line using its slope and intercept

Choose the most convenient method to graph a line

Graph and interpret applications of slope–intercept

Use slopes to identify parallel lines

Use slopes to identify perpendicular lines

Answer:

the percentage of  bearings   that will  not be acceptable = 7.3%

Step-by-step explanation:

Given that:

Mean = 0.499

standard deviation = 0.002

if the true average diameter of the bearings it produces is 0.500 in and bearing is acceptable if its diameter is within 0.004 in.

Then the ball bearing acceptable range = (0.500 - 0.004, 0.500 + 0.004 )

= ( 0.496 , 0.504)

If x represents the diameter of the bearing , then the probability for the  z value for the random variable x with a mean and standard deviation can be computed as follows:

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - \mu}{\sigma} \leq \dfrac{X -\mu}{\sigma} \leq \dfrac{0.504 - \mu}{\sigma})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - 0.499}{0.002} \leq \dfrac{X -0.499}{0.002} \leq \dfrac{0.504 - 0.499}{0.002})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{-0.003}{0.002} \leq Z \leq \dfrac{0.005}{0.002})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (-1.5 \leq Z \leq 2.5)[/tex]

[tex]P(0.496\leq X \leq 0.504) = P (-1.5 \leq Z \leq 2.5)[/tex]

[tex]P(0.496\leq X \leq 0.504) = P(Z \leq 2.5) - P(Z \leq -1.5)[/tex]

From the standard normal tables

[tex]P(0.496\leq X \leq 0.504) = 0.9938-0.0668[/tex]

[tex]P(0.496\leq X \leq 0.504) = 0.927[/tex]

By applying the concept of probability of a  complement , the percentage of bearings will now not be acceptable

P(not be acceptable)  = 1 - P(acceptable)

P(not be acceptable)  = 1 - 0.927

P(not be acceptable)  = 0.073

Thus, the percentage of  bearings   that will  not be acceptable = 7.3%

Answer:

45

Step-by-step explanation:

because 5•9=45 so yeah that's the answer

Answer:

x= i√30

Step-by-step explanation:

I'm going to go into this under the assumption that you've covered imaginary numbers based on the question. If I'm wrong then sorry about that.

Okay, so first you want to subtract 30 from both sides

x^2=-30

Then you take the square root of each side.

√(x^2)=√-30

x=√-30

Since it's impossible to square a number to get a negative number, you'll end up with an imaginary number. You have to rewrite x=√-30 to get rid of the negative sign under the radical. Rewriting this will also indicate that it's an imaginary number.

Final answer: x = i√30

Answer:

Step-by-step explanation:

-we know :

we must have the same unit on the distance traveled in order to be able to compare distances  

1 mile = 1.6 kilometers

-Angelique traveled 75 miles ( 120 kilometers)

75 miles = 1.6 *75 = 120 kilometers

-Jamila traveled 115 kilometers  is given in the problem

-Angelique has travelled further than Jamila because

120 kilometers > 115 kilometers

Answer:

No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4

Step-by-step explanation:

Equations : x + y + z = 17 [ Total times taken to score ]

1x + 2y + 3z = 33 [ Total Score ]

Also, y = x + 3

Putting the value of 'y' in both equations :

x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14  (i)

1x + 2 (x + 3) + 3z = 33 →  x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)

Solving these equations :

From (i), z = 14 - 2x

Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27

42 - 3x = 27 → 3x = 15 → x = 5

y = x + 3 = 5 + 3 → y = 8

z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4

Answer:

4

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Question:

Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to buy 50kg of corn in total for her next order. White corn costs $0.30 per kilogram, yellow corn costs $0.15 per kilogram, and she wants to spend $12 total.

What does point F represent in this context?

Answer:

Marcelina spends less that the intended amount of money and buy less than enough corn

Split up the boundary of C (which I denote ∂C throughout) into the parabolic segment from (1, 1) to (0, 0) (the part corresponding to y = x ²), and the line segment from (1, 1) to (0, 0) (the part of ∂C on the line y = x).

Parameterize these pieces respectively by

r(t) = x(t) i + y(t) j = t i + t ² j

and

s(t) = x(t) i + y(t) j = (1 - t ) i + (1 - t ) j

both with 0 ≤ t ≤ 1.

The circulation of F around ∂C is given by the line integral with respect to arc length,

[tex]\displaystyle \int_{\partial C}\mathbf F\cdot\mathbf T \,\mathrm ds[/tex]

where T denotes the tangent vector to ∂C. Split up the integral over each piece of ∂C :

• on the parabolic segment, we have

T = dr/dt = i + 2t j

• on the line segment,

T = ds/dt = -i - j

Then the circulation is

[tex]\displaystyle \int_{\partial C}\mathbf F\cdot\mathbf T\,\mathrm ds = \int_0^1 (7t^3\,\mathbf i+5t^4\,\mathbf j)\cdot(\mathbf i+2t\,\mathbf j)\,\mathrm dt + \int_0^1 (7(1-t)^2\,\mathbf i+5(1-t)^2\,\mathbf j)\cdot(-\mathbf i-\mathbf j)\,\mathrm dt \\\\ = \int_0^1 (7t^3+10t^5)\,\mathrm dt - 12 \int_0^1 (1-t)^2\,\mathrm dt =\boxed{-\frac7{12}}[/tex]

Alternatively, we can use Green's theorem to compute the circulation, as

[tex]\displaystyle\int_{\partial C}\mathbf F\cdot\mathbf T\,\mathrm ds = \iint_C\frac{\partial(5y^2)}{\partial x} - \frac{\partial(7xy)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = -7\int_0^1\int_{x^2}^x x\,\mathrm dx \\\\ = -7\int_0^1 xy\bigg|_{y=x^2}^{y=x}\,\mathrm dx \\\\ =-7\int_0^1(x^2-x^3)\,\mathrm dx = -\frac7{12}[/tex]

The flux of F across ∂C is

[tex]\displaystyle \int_{\partial C}\mathbf F\cdot\mathbf N \,\mathrm ds[/tex]

where N is the normal vector to ∂C. While T = x'(t) i + y'(t) j, the normal vector is N = y'(t) i - x'(t) j.

• on the parabolic segment,

N = 2t i - j

• on the line segment,

N = - i + j

So the flux is

[tex]\displaystyle \int_{\partial C}\mathbf F\cdot\mathbf N\,\mathrm ds = \int_0^1 (7t^3\,\mathbf i+5t^4\,\mathbf j)\cdot(2t\,\mathbf i-\mathbf j)\,\mathrm dt + \int_0^1 (7(1-t)^2\,\mathbf i+5(1-t)^2\,\mathbf j)\cdot(-\mathbf i+\mathbf j)\,\mathrm dt \\\\ = \int_0^1 (14t^4-5t^4)\,\mathrm dt - 2 \int_0^1 (1-t)^2\,\mathrm dt =\boxed{\frac{17}{15}}[/tex]

Answer:

±7 sqrt(2) = x

Step-by-step explanation:

98 - x^2 = 0

Add x^2 to each side

98 =x^2

Take the square root of each side

±sqrt(98) = sqrt(x^2)

±sqrt(49*2) = x

±7 sqrt(2) = x

Answer:

[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]

Step-by-step explanation:

[tex]98-x^2 =0[/tex]

[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]

[tex]98=x^2[/tex]

[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]

[tex]\pm \sqrt{98} =x[/tex]

[tex]\sf Simplify \ radical.[/tex]

[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]

[tex]\pm 7\sqrt{2} =x[/tex]

[tex]\sf Switch \ sides.[/tex]

[tex]x= \pm 7\sqrt{2}[/tex]

Answer:

D

Step-by-step explanation:

The ratio of yellow paint to blue paint is 4:3. We can make the largest amount of green paint by using all of the 20 quarts of yellow paint so we have to solve for x in 4:3 = 20:x, since 4 * 5 = 20, 3 * 5 = x so we use 15 qts of blue paint, therefore we will have 20 + 15 = 35 qts of green paint.

Answer:

D

Step-by-step explanation:

Let numbers be x and y

ATQ

Adding both

[tex]\\ \sf\longmapsto 2x=58[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{58}{2}[/tex]

[tex]\\ \sf\longmapsto x=29[/tex]

Now putting value in eq(2)

[tex]\\ \sf\longmapsto x-y=9[/tex]

[tex]\\ \sf\longmapsto 29-9=y[/tex]

[tex]\\ \sf\longmapsto y=20[/tex]

Answer:

 At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

Step-by-step explanation:

From the question we are told that

   The  population mean is [tex]\mu = 60 \ hr[/tex]

    The sample size is  [tex]n = 16[/tex]

    The  sample mean is  [tex]\= x = 68 \ hr[/tex]

     The  standard deviation is  [tex]\sigma = 20 \ hr[/tex]

The  null hypothesis is  [tex]H_o : \mu = 60[/tex]

The  alternative [tex]H_a : \mu > 60[/tex]

Here we would assume the level of significance of this test to be  

         [tex]\alpha = 5\% = 0.05[/tex]

Next we will obtain the critical value of the level of significance from the normal distribution table, the value is    [tex]Z_{0.05} = 1.645[/tex]

  Generally the test statistics  is mathematically represented as

           [tex]t = \frac{ \= x - \mu}{ \frac{ \sigma }{\sqrt{n} } }[/tex]

substituting values

           [tex]t = \frac{ 68 - 60 }{ \frac{ 20 }{\sqrt{16} } }[/tex]

          [tex]t = 1.6[/tex]

Looking at the value of t and  [tex]Z_{\alpha }[/tex] we see that [tex]t< Z_{\alpha }[/tex] hence we fail to reject the null hypothesis

   This means that there no sufficient evidence to conclude that it takes more than 60 hours to complete the course

So

   At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

Answer:

3x - 4

Step-by-step explanation:

As Tina's age is 3 into x ( 3 x x= 3x)but 4years less (-4)

Therefore Tina's age is 3x - 4

Answer:

3x - 4

Step-by-step explanation:

Use these representations:  niece's age: x

We triple x and then subract 4 years from the result, obtaining:

Tina's age:  3x - 4

Question options :

A. There is sufficient evidence to reject the claim

u < 99.

B. There is sufficient evidence to support the claim

u < 99.

C. There is not sufficient evidence to reject the claim

u < 99.

D. There is not sufficient evidence to support the claim

u< 99.

Answer:

B. There is sufficient evidence to support the claim

u < 99.

Step-by-step explanation:

We construct the n*ll and alternative hypotheses to support our claim

The n*ll hypothesis :H0

The alternative hypothesis : Ha

N*ll hypothesis =H0: u=99

Alternative hypothesis =Ha: u<99

So if n*ll hypothesis (H0) u=99 is rejected, then we accept the alternative hypothesis that u<99

we can therefore have sufficient evidence to support our claim that u<99

Answer:

12). LM = 37.1 units

13). c = 4.6 mi

Step-by-step explanation:

12). LM² = 23² + 20² - 2(23)(20)cos(119)°

    LM² = 529 + 400 - 920cos(119)°

    LM² = 929 - 920cos(119)°

    LM = [tex]\sqrt{929+446.03}[/tex]

          = [tex]\sqrt{1375.03}[/tex]

          = 37.08

          ≈ 37.1 units

13). c² = 5.4² + 3.6² - 2(5.4)(3.6)cos(58)°

    c² = 29.16 + 12.96 - 38.88cos(58)°

    c² = 42.12 - 38.88cos(58)°

    c = [tex]\sqrt{42.12-20.603}[/tex]

    c = [tex]\sqrt{21.517}[/tex]

    c = 4.6386

    c ≈ 4.6 mi

Answer:

  The approximate standard error of the sample proportion is [tex]SE = 0.0454[/tex]

Step-by-step explanation:

From the question we are told that

      The  sample proportion is  [tex]\r p = 0.29[/tex]

       The  sample size is  n =  100

Generally the standard error of the sample proportion is mathematically represented as

         [tex]SE = \sqrt{ \frac{ \r p (1- \r p )}{n} }[/tex]

substituting values    

         [tex]SE = \sqrt{ \frac{ 0.29 (1- 0.29 )}{ 100 } }[/tex]

         [tex]SE = 0.0454[/tex]

Answer:

6+2+9+5+2+3+6+3 = 36

Step-by-step explanation:

If you like my answer than please mark me brainliest

Answer:

Step-by-step explanation:

This problem is on the mensuration of solid shapes, an oblique cylinder.

the expression for the volume of an oblique cylinder is given as

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

Given data

radius r= 5

height h= 12, and

slant length of 13.

Substituting the given data into the expression we can solve for the volume below

[tex]volume= \pi* 5^2*12\\\ volume= \pi*25*12\\\ volume= \pi*300\\\ volume= 300\pi[/tex]

Answer:

300

Step-by-step explanation: