What is the value of…
–13
–12
12
13

Answer:

x = -8, 1

Step-by-step explanation:

Hi there!

[tex]x^2+7x=8[/tex]

Move 8 to the other side:

[tex]x^2+7x-8=8-8\\x^2+7x-8=0[/tex]

Now, we can ask ourselves: what two factors of -8 add to 7? Those two numbers would be 8 and -1. Knowing this, factor:

[tex](x+8)(x-1)=0[/tex]

Because of the zero product property (that states that if the product of two numbers is 0, then one of the numbers must be equal to 0), we can find the solutions to the quadratic by setting each term equal to 0:

[tex]x+8=0\\x=-8[/tex]    

[tex]x-1=0\\x=1[/tex]

Therefore, the solutions of the quadratic are -8 and 1.

I hope this helps!

Answer:

15/4

Step-by-step explanation:

sin60 =z/15

z=15sin60 =(15√3)/2

cos30 =b/z

b = zcos30 = (15√3)/2 * √3/2 = 45/4

a = 15-b = 15-45/4 = 15/4

The value of a is 15/4

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

According to the given figure,

Here is a right triangle

Let, The hypotenuse = 15

perpendicular = z and base = 15 = a + b

⇒ sin60 = perpendicular/hypotenuse = z/15

⇒ z = 15sin60 = (15√3)/2

⇒ cos30 = base/hypotenuse = b/z

⇒ b = zcos30 = (15√3)/2 * √3/2 = 45/4

⇒ a + b = 15

Substitute the value of b in the above equation,

⇒ a = 15-b = 15-45/4 = 15/4

Hence, the value of a is 15/4.

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Answer:

a.) 1908.30

b.) 96373.15

c.)302491.15

unrounded answers below

Step-by-step explanation:

The amount that is to be loaned out is 380000-110000=270000

The effective montly rate is .07/12=.005833333

a.)

[tex]270000=x(\frac{1-(1+.005833333)^{-(25*12)}}{.005833333})=1908.303833[/tex]

b.)

use what is called the prospective method (the outstanding loan balance at time n is equal to the present value of the remaining payments)

[tex]1908.303833(\frac{1-(1+.005833333)^{-(25*12-20*12)}}{.005833333})=96373.14775[/tex]

c.)

total paid= 1908.303833*12*25=572491.1499

amount of loan: 270000

Total interest paid:

572491.1499-270000=302491.1499

Answer: 20.5

Step-by-step explanation:

Cos 43 = X/28

O.73 = x/28

(0.73)(28)=20.5

Answer: 1/6

Step-by-step explanation:

Given:

4/9 and 11/18

Solve:

STEP ONE: Make the denominators equal by determining the LCM

LCM = Least Common Multiple

First Five multiples of 9 = 9, 18, 27, 36, 45

First FIve multiples of 18 = 18, 36, 54, 72, 90

As we can see from the list above, both 18 and 36 overlap, however, 18 is less than 36. Therefore, 18 is the LCM.

STEP TWO: Compare the size and determine the greater one.

4/9 = (4 × 2) / (9 × 2) = 8/18

11/18 = 11/18

Since 11 > 8, therefore, 11/18 is greater than 8/18

STEP THREE: Find the difference between the two fractions.

 11/18 - 4/9

=11/18 - 8/18

=(11 - 8) / 18

= 3 / 18

= 1/6

Hope this helps!! :)

Please let me know if you have any questions

Answer:

0

Step-by-step explanation:

0

The value of x and y is C) x=90°, y=24°.

Trigonometric ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

various ratios are:-

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric.

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Answer:

H0 : The variables are independent

H1 : The variables are not independent

Step-by-step explanation:

In a Chisquare test ; The null hypothesis is used to lay claim that the variables are independent, that is no relationship exists between the categorical variables in the population while the alternative hypothesis negates the null thus claiming that the variables aren't independent.

The null hypothesis, H0 : The variables are independent, A = B = C

The alternative hypothesis ; H1 : The variables are not independent, A ≠ B ≠ C

Answer:

1,125 households would have pets in the area.

Step-by-step explanation:

We have 1,500 total households. We also know that 3/4 (or 0.75) of these households have pets. We would multiply 1,500 by 0.75 (which is equal to 3/4), resulting in 1,125. Therefore, 1,125 households would have pets in the area.

Answer:

1125 households

Step-by-step explanation:

3/4 of total households in area = # of households that have pets in the area

3/4 of 1500 = # of households that have pets in the area

3/4 · 1500 = # of households that have pets in the area

75/100 · 1500 = # of households that have pets in the area

0.75 · 1500 = 1125

1125 households

Answer:

10 gallons

Step-by-step explanation:

84 ÷ 6.5 =12.9(The unit rate.)

Seeing as one gallon can get you 12.9 miles;

126÷12.9=9.7

So the answers 9.7 gallons, but if you need to round, then 10 to get a whole number.

Answer:

9.75

Step-by-step explanation:

We can write a ratio to solve

84 miles          126 miles

--------------   = -------------------

6.5 gallons        x gallons

Using cross products

84 x = 6.5 * 126

84x=819

84x/84 = 819/84

x = 9.75

Answer:

3/56

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome.

Given that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles.

The total number of marbles in the box

= 1 + 3 + 2 + 2

= 8 marbles

The probability that the first marble is white and the second marble is blue

= 3/8 * 1/7

= 3/56

Answer:

[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]

Step-by-step explanation:

Given

[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]

Required

Determine [tex]\cos(\theta)[/tex]

We have:

[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]

Split

[tex]\tan(\theta) = -\frac{\sqrt{19}}{\sqrt{17}}[/tex]

tan is calculated as:

[tex]\tan(theta) = \frac{opposite}{adjacent}[/tex]

So:

[tex]Opposite = -\sqrt{19[/tex]

[tex]Adjacent = \sqrt{17[/tex]

And:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex] --- Pythagoras theorem

[tex]Hypotenuse^2 = (-\sqrt{19})^2 + (\sqrt{17})^2[/tex]

[tex]Hypotenuse^2 = 19 + 17[/tex]

[tex]Hypotenuse^2 = 36[/tex]

Take square roots

[tex]Hypotenuse = 6[/tex]

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos(\theta) = \frac{\sqrt{17}}{6}[/tex]

Since it is in the second quadrant, then:

[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]

Answer:

gshwhsye

Step-by-step explanation:

gshshhshshshjsjsjsj

Answer:

x = 2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Pytago:

[tex]2^2 + 4^2 = x^2\\x = \sqrt{2^2 + 4^2} \\x = 2\sqrt{5}[/tex]

Answer:

4.47

Step-by-step explanation:

x²= 2² + 4²

x² = 4 + 16

x²= 20

x = √20

x= 4.47

Answer:

B. 550

Step-by-step explanation:

550 is the smallest number that becomes 600 when rounded to the nearest hundred

Answer:

L(x)=-4x+9

L(2.1)=0.6

Step-by-step explanation:

It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.

Theb use this to estimate f(2.1).

To find slope of tangent line, we must differentiate and then plug in 2 for x.

f'(x)=0-2x by constant and power rule.

f'(x)=-2x

So the slope of the tangent line is -2(2)=-4.

A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.

f(2)=5-(2)^2

f(2)=5-4

f(2)=1

So let's rephrase the question a little.

What's the equation for a line with slope -4 and goes through point (2,1).

Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.

Plug in our information: y-1=-4(x-2).

Distribute: y-1=-4x+8

Add 1 on both sides: y=-4x+9

Let's call this equation L(x), an expression to approximate value for f near x=2.

L(x)=-4x+9

Now the appropriation at x=2.1:

L(2.1)=-4(2.1)+9

L(2.1)=-8.4+9

L(2.1)=0.6

If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.

B

Should be the answer

Answer:

ask in English then I can help u

N is the midpoint of MO and NO is 5, so MN would also be 5

MP = MN + NP = 5 + 9 = 14

Answer:

6:21

Step-by-step explanation:

We want to find the ratio of squares to shapes

So simply count the squares

There are 6 squares

And then find the total number of shapes

There are a total of 21 shapes

So for every 6 squares there are 21 total shapes

In other words the ratio of squares to shapes is 6:21

Answer:

Step-by-step explanation:

Given,

Number of squares = 6

Total no. of shapes = 21

Therefore,

Unsimplified ratio of squares to total shapes

= 6:21 (Ans)

Answer:

2

Step-by-step explanation:

33

the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.

The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.

In terms of hyperbola, F1F2=2c, c=20.

The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.

Use formula c^2=a^2+b^2c

2

=a

2

+b

2

to find b:

\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}

(20)

2

=(18)

2

+b

2

,

b

2

=400−324=76

.

The branches of hyperbola go in y-direction, so the equation of hyperbola is

\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1

b

2

y

2

−

a

2

x

2

=1 .

Substitute a and b:

\dfrac{y^2}{76}- \dfrac{x^2}{324}=1

76

y

2

−

324

x

2

=1 .

Answer:

both

Step-by-step explanation:

Congruent shapes have equal corresponding side lengths

The true statement is (c) both

To map the quadrilaterals on one another, then the sequence of transformation must be rigid transformation

The given sequence of transformations are both rigid, and they both would map quadrilaterals STUV and ABCD

Hence, the true statement is (c) both

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Answer:

1

5

=

8

2

−

1

4

15=8x^{2}-14x

15=8x2−14x

1

5

−

(

8

2

−

1

4

)

=

0

Step-by-step explanation:

=

−

3

4

=

5

2

The solution of equation is x =5/2  or  x= -3/4.

A number or other mathematical object is factored (or factorised, see variants in spelling in English) or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.

We have,

Equation: 15 = 8x² - 14x

Now, rearranging the equation as

8x² -14x -15 = 0

8x² - 20x + 6x -15=0

4x( 2x - 5) + 3 (2x-5)= 0

(2x-5)(4x +3)= 0

2x-5 =0  or 4x+ 3= 0

x =5/2  or  x= -3/4

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Answer: 0, 5

Step-by-step explanation: a translation is just like sliding the object in this case a triangle/point on the triangle. so the point it is at now is -2, 5 because it is 2 to the left and 5 up. and if you go to the right 2. then you are adding 2 to the x value. so -2 +2 = 0. which is how you get 0, 5

Answer:

Hence the correct option is option c has a Binomial distribution with n=21 and p=50%.

Step-by-step explanation:

1)  

A coin is tossed 19 times,  

P(Head)=0.5  

P(Tail)=0.5  

We have to find the probability of a total number of heads in all the coin tosses equals 9.  

This can be solved using the binomial distribution. For binomial distribution,  

P(X=x)=C(n,x)px(1-p)n-x  

where n is the number of trials, x is the number of successes, p is the probability of success, C(n,x) is a number of ways of choosing x from n.  

P(X=9)=C(19,9)(0.5)9(0.5)10  

P(X=9)=0.1762  

2)  

A fair die is rolled twice.  

Total number of outcomes=36  

Possibilities of getting sum as 9  

S9={(3,6),(4,5)(5,4),(6,3)}  

The total number of spots showing in all the die rolls equals 9 =4/36=0.1111  

3)  

The event of getting a good number of spots on a die roll is actually no different from the event of heads on a coin toss since the probability of a good number of spots is 3/6 = 1/2, which is additionally the probability of heads. the entire number of heads altogether the tosses of the coin plus the entire number of times the die lands with a good number of spots has an equivalent distribution because the total number of heads in 19+2= 21 tosses of the coin. The distribution is binomial with n=21 and p=50%.

1) Seven less than twice a number, n, is 32.

ANS) B. 2n - 7 = 32

Answer:

1.

B. 2n - 7 = 32 is the right answer

Answer:

~1383.5 meters cubed

Step-by-step explanation:

(17.6 x 17.6 x 13.4) ÷ 3 = ~1383.5