Suppose an angle has a measure of x degrees. What is the measure of the angle that is five times as large as the first angle? If the two angles are supplementary, what equation can you write using the measures of the angles? What are the measures of the two angles?

Answer:

a) E

b) line segment AB

Step-by-step explanation:

a) E

b) line segment AB (It's AB with the line over it - no arrowheads)

Answer:

In bold below.

Step-by-step explanation:

(a) The largest angle is opposite the largest side.

So by the Cosine Rule:

8^2 = 4^2 + 6^2 - 2*4*6 cos x

cos x =  (8^2 - 4^2 - 6^2) / (-2*4* 6)

= -0.25.

x = 104.48 degrees.

(b) Area of the triangle = 1/2 * 4 * 6 sin 104.48

= 11.62

= 3 √15.

(c)  The shortest altitude will have the longest sides as the base.

Area = 1/2 * altitude * base

3√15 = 1/2 * 8 * a

a = 3√15 / 4 cm

= 0.75√15 cm.

The cosine of the largest angle is 104.48 degrees

The area of the triangle is 3√15cm² is 3 √15

The length of the shortest altitude of the triangle​ is 0.75√15 cm.

A triangle can be defined as a figure that has three lines. It can be of various dimensions it can a scale as Pythagoras or an isosceles triangle. They all have different properties.

(a)

With the help of the Cosine Rule:

[tex]8^2[/tex] = [tex]4^2 + 6^2 - 2 \times 4\times6 cos x[/tex]

cos x = [tex](8^2 - 4^2 - 6^2) / (-2 \times 4 \times 6)[/tex])

= -0.25.

x = 104.48 degrees.

(b)

Area of the triangle

=[tex]1/2 \times 4 \times 6 sin 104.48[/tex]

= 11.62

= 3 √15.

(c)  

Area =[tex]1/2 \times altitude \times base[/tex]

3√15 = 1/2 * 8 * a

a = 3√15 / 4 cm

= 0.75√15 cm.

Learn more about triangle, here:

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Answer:

Yes -15.5 is a rational number

Step-by-step explanation:

A rational number is a number that can be in the form p/q

where p and q are integers and q is not equal to zero.

-15.5 can easily be converted to fraction form which is = [tex]\frac{31}{2}[/tex]

Hope this helps you! :)

Answer:

Yes

Step-by-step explanation:

-15.5 can be rewritten as -155/10, which is a rational number.  Yes.

Furthermore, -155/10 can be reduced to the equivalent

-31/2

Answer:

a. is false

Step-by-step explanation:

4 liters= 1.057 gal

1.057 is greater than 1

Hope this helps :)

Step-by-step explanation:

Remember:

X = 2.5

Y = 1.5

Z = 1

The chart:

         X             Y           Z

I      10000    7000    8000

II     6000     10000   5000

X

The first column represents X. Since X's value is 2.5, we multiply both those numbers by 2.5.

[tex]10,000*2.5=25,000[/tex]

[tex]6000*2.5=15,000[/tex]

These are the values of X.

Y

The second column represents Y. Since Y's value is 1.5, we multiply both of the values by 1.5.

[tex]7,000*1.5=10,500[/tex]

[tex]10,000*1.5 = 15,000[/tex]

These are the values of Y.

Z

The last column represents Z. Since Z's value is 1, we do not need to multiply the numbers, since they are already multiplied by 1.

[tex]8,000[/tex]

[tex]5,000[/tex]

These are the values of Z.

ADDING

Now that we have are 6 numbers solved, all we have to do is add them all together.

[tex](25+15+10.5+15+8+5)\\25,000+15,000+10,500+15,000+8,000+5,000=78,500[/tex]

Our final answer: $78,500 is the total. (first option)

Answer:

to the right of x = 2 the function is increasing

{ x | x > 2}

Step-by-step explanation:

Recall that this is a quadratic function, and therefore responds to the shape of a parabola. In this case is also a parabola with branches opening up since the coefficient of the square term is positive. So, we just need to find where the vertex is located, and we know that to the left of the x-value of the vertex the function is decreasing, and to the right of it the function is increasing.

The formula for the x of the vertex of a parabola of the form:

[tex]y=ax^2+bx+c[/tex]

is  [tex]x_{vertex}=\frac{-b}{2\,a}[/tex]

which in our case gives:

[tex]x_{vertex}=\frac{-b}{2\,a} =\frac{4}{2} =2[/tex]

Therefore, to the left of x = 2 the function decreases , and to the right of x = 2 the function is increasing.

Answer:

square root of 1.9321 = 1.39

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

So we have:

[tex]g(x)=x^2+3x-1[/tex]

To find g(5), substitute 5 for x:

[tex]g(5)=(5)^2+3(5)-1[/tex]

Square and multiply:

[tex]g(5)=25+15-1[/tex]

Add:

[tex]g(5)=40-1[/tex]

Subtract:

[tex]g(5)=39[/tex]

So, our answer is B :)

Answer: OPTION 2. 39

Step-by-step explanation:

g(x)=x²+3x-1 ⇔ Given

g(5)=(5)²+3(5)-1 ⇔ Plug the value of x in (5)

g(5)=25+15-1 ⇔ do all the operation (square, multiplication, etc.)

g(5)=40-1 ⇔ combine like term (first do the first two)

g(5)=39 ⇔ combine like term

Hope this helps!! :)

Please let me know if you have any question

Answer:

gay

Step-by-step explanation:

i mean it starts with a g doesnt it?

Answer:

google?

Step-by-step explanation:

There are can be can be many things found on the pages starting with the letter g.

Answer:

x=0

Step-by-step explanation:

4(x-5) = 4(4+x)

4x-20 = 16+4x

4x-4x = 16+20

0x=36

x = 36/0

x = 0

hope it might help

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Answer:

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].

Step-by-step explanation:

There are two kew parameters for a sphere: Center ([tex]h[/tex], [tex]k[/tex], [tex]s[/tex]) and Radius ([tex]r[/tex]). The radius is the midpoint of the line segment between endpoints. That is:

[tex]C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2} \right)[/tex]

[tex]C(x,y,z) = (1,-2,4)[/tex]

The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:

[tex]r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}[/tex]

[tex]r = 10\sqrt{3}[/tex]

The general formula of a sphere centered at (h, k, s) and with a radius r is:

[tex](x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}[/tex]

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].

Answer:

[tex]y = 5\cdot e^{2.3\cdot x}[/tex]

Step-by-step explanation:

A semilog plot consist in a logarithmic axis and a linear axis. In this case, the only equation that fulfill the statement conditions of a semilog plot is [tex]y = 5\cdot e^{2.3\cdot x}[/tex], as it is proved below:

1) [tex]y = 5\cdot e^{2.3\cdot x}[/tex] Given

2) [tex]y = \ln (5\cdot e^{2.3\cdot x})[/tex] Semilog plot

3) [tex]y = \ln 5 + \ln e^{2.3\cdot x}[/tex] [tex]\ln (a\cdot b) = \ln a + \ln b[/tex]

4) [tex]y = \ln 5 + 2.3\cdot x \cdot \ln e[/tex] [tex]\ln a^{b} = b\cdot \ln a[/tex]

5) [tex]y = \ln 5 + 2.3\cdot x[/tex] [tex]\ln e = 1[/tex]/Modulative property/Result

Answer:

D

Step-by-step explanation:

So we know that:

[tex]\cos(A)=1/3[/tex]

To co-function identities state that:

[tex]\cos(\theta)=\sin(90\textdegree-\theta)[/tex]

Therefore, this is the same as:

[tex]\cos(A)=\sin(90\textdegree-A)[/tex]

B is correct.

Additionally, recall that in a right triangle, the two other angles must add up to 90. In other words:

[tex]A+B=90[/tex]

Subtract A from both sides:

[tex]B=90-A[/tex]

So we can make the substitution:

[tex]\sin(90-A)=\sin(B)[/tex]

Thus, A is also correct.

The correct answer is D .

Answer:D

Step-by-step explanation:

So we know that:

To co-function identities state that:

Therefore, this is the same as:

B is correct.

Additionally, recall that in a right triangle, the two other angles must add up to 90. In other words:

Subtract A from both sides:

So we can make the substitution:

Thus, A is also correct.

The correct answer is D .

Answer:

1819

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Round 4.038 down to 4

Round 5.5 up to 6

Round 2.17 to 2

4+6+2 = 12

Answer:

The number to be subtracted = -11/2

Step-by-step explanation:

(3*rational number)-x=1/2

The rational number given = -5/3

Then thrice the rational number

= 3*rational number

= 3*(-5/3)

= -5

(3*rational number)-x=1/2

-5-x= 1/2

-5- 1/2= x

-11/2= x

The number to be subtracted = -11/2

Answer:

No it is not satisfied

Step-by-step explanation:

The one-way ANOVA is used to measure whether the difference between the means of two independent groups are statistically significant.

For it to be satisfied, there has to be one independent variable which is categorical and one dependent variable. The dependent variable on its own has to be a continuous variable

The assumptions are:

1. Equal variance between population

2. Independence between observations

3. The random samples have to be gotten from a normal population.

Answer:

16 degrees

Step-by-step explanation:

Add 20 to -4

-4 + 20

= 16

So, the temperature at noon was 16 degrees

Answer:

16 degrees

Step-by-step explanation:

The question states that it increased +20 degrees by noon from 6:00 am. So,

-4 + 20 = 16

The temp would be 16 degrees at noon.

Answer:

x² + xy - 6y²

Step-by-step explanation:

FOIL

(x+3y)(x-2y)

F= x²

O= -2xy

I= 3xy

L= -6y²

Add these together = x² + xy - 6y²

Step-by-step explanation:

Hey, there!

Let me simply clear you.

While multiplying algebraic expression, you must be very careful about sign and brackets.

Here,

[tex](x + 3y)(x - 2y)[/tex]

Let's multiply (x-2y) by (x+3y)

[tex] = x(x - 2y) + 3y(x - 2y)[/tex]

[tex] = ({x}^{2} - 2xy) + (3xy - 6 {y}^{2}) [/tex]

Open brackets.

[tex] = {x}^{2} - 2xy + 3xy - 6 {y}^{2} [/tex]

Simplify the like terms.

[tex] = {x}^{2} + xy - 6 {y}^{2} [/tex]

Therefore, the answer is x^2 + xy- 6y^2.

Hope it helps.....

Answer:

1) 1

2) (2,3)

3) x⁴

Step-by-step explanation:

1)

We have the expression:

[tex]7x+1[/tex]

The degree of an equation is the largest exponent of the equation.

We can rewrite our expression as:

[tex]=7x^1+1x^0[/tex]

1 is the largest exponent.

Thus, our degree is 1.

2)

We have the system of equations:

[tex]x+y=5\\3x-y=3[/tex]

To solve, we can use substitution.

From the first equation, subtract x from both sides:

[tex]y=5-x[/tex]

Substitute this into the second equation:

[tex]3x-(5-x)=3[/tex]

Simplify:

[tex]3x-5+x=3[/tex]

Add 5 to both sides:

[tex]3x+x=8[/tex]

Combine like terms:

[tex]4x=8[/tex]

Divide both sides by 4:

[tex]x=2[/tex]

So, x is 2.

Substitute this back into the first equation:

[tex]x+y=5[/tex]

Substitute x for 2:

[tex]2+y=5[/tex]

Subtract 2 from both sides:

[tex]y=3[/tex]

Our solution is (2,3)

3)

We have the expression:

[tex]\frac{x^4}{x^0}[/tex]

Anything to the zeroth power (except for 0) is 1. Assuming x is not 0:

[tex]=x^4/1\\=x^4[/tex]

And that's the simplest it can get.

Answer:

[tex]\Huge \boxed{\mathrm{1. \ 1}} \\ \\ \\ \Huge \boxed{\mathrm{2. \ (2,3)}} \\\\\\ \Huge \boxed{{3. \ x^4 }}[/tex]

Step-by-step explanation:

The degree is the largest exponent on the variable.

[tex]7x^1 + 1x^0[/tex]

The largest exponent on the variable is 1.

The degree is 1.

System of equations:

[tex]x+y=5 \\ \\ 3x-y=3[/tex]

Solving y for the first equation.

Subtracting x from both sides.

[tex]y=5-x[/tex]

Substitution method.

[tex]3x-(5-x)=3[/tex]

Distribute negative sign.

[tex]3x-5+x=3[/tex]

Combining like terms.

[tex]4x-5=3[/tex]

Adding 5 to both sides.

[tex]4x=8[/tex]

Dividing both sides by 4.

[tex]x=2[/tex]

Substitution method.

[tex]y=5-2 \\ \\ \\ y=3[/tex]

[tex]\displaystyle \frac{x^4 }{x^0 }[/tex]

Subtract exponents with same bases when dividing.

[tex]x^{4-0}[/tex]

[tex]x^4[/tex]

Answer:

15 + 2.05 x = 2.35 x

Step-by-step explanation:

Let x be the number of gallons you would have to buy for the two places to be the same.

At the club, there is a monthly fee of $15 that is charged once in a month. They also charge $2.05 per gallon, which is charged every gallon of gas you buy.

We can write an expression: 15 + 2.05 x

At the gas station, they charge $2.35 per gallon with no other fees.

We can also write an expression: 2.35 x

For the prices to be the same, we have 15 + 2.05 x = 2.35 x

If we were to solve, then we have:

(2.35 - 2.05) x = 15

x = 15 / 0.3 = 50 gallons

Answer:

-6w + 11wy + 6 - 4y

Step-by-step explanation:

Step 1: Write out expression

-6w + 9wy + 6 + 2wy - 4y

Step 2: Combine like terms

-6w + 11wy + 6 - 4y

Answer:

11wy-6w-4y+6

Step-by-step explanation:

−6w + 9wy + 6 + 2wy − 4y

Combine like terms

−6w  + 6 + 2wy+ 9wy − 4y

11wy-6w-4y+6

Answer:

Interest for the month = $12.25

Step-by-step explanation:

Given:

Amount in bank = $700

Rate of interest per month = 21% / 12 = 0.0175

Find:

Interest for the month

Computation:

Interest for the month = Amount in bank × Rate of interest per month

Interest for the month = $700 × 0.0175

Interest for the month = $12.25

Answer: Option 1. irrational number, nonrepeating decimal

Step-by-step explanation:

the simplified version of √32 is 4√2

√2 is not a rational number since it can't be written in the form of fraction, so √32 is also irrational.

√2 is equal to 1.414213562... this is nonrepeating, which means, √32 is nonrepeating.

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer: 49

Step-by-step explanation:

We know, x = -2

Substituting value of x in [tex]8x^{2} -7x+3[/tex],

[tex]8(-2)^{2} - 7(-2) + 3\\=8(4) -7(-2) + 3\\=32+14+3\\=49[/tex]

Answer:

f(-2)=8*(-2)^2-7*(-2)+3=8*4+14+3=32+17=49

Step-by-step explanation:

Answer:

71, 72, 73

Step-by-step explanation:

So we want to find three consecutive integers that equal 216.

Let the first integer be n.

Then the second integer is n+1, and the third integer is n+2.

Thus:

[tex]n+(n+1)+(n+2)=216[/tex]

Combine like terms:

[tex]3n+3=216[/tex]

Subtract 3 from both sides:

[tex]3n=213\\[/tex]

Divide 3 from both sides:

[tex]n=71[/tex]

So, the first term is 71.

And the other two is 72 and 73.

And we are done :)

Answer: 60

Step-by-step explanation:

[tex]A = s^2\\\\frac{dA}{dt}=2s \frac{ds}{dt}\\36=s^2 \\ s=6\\\frac{dA}{dt} = 2(6)(5)=60 \frac{cm^2}{s}[/tex]

Answer:

The area of the square is increasing at a rate of 60 cm²/s

Step-by-step explanation:

Let [tex]l[/tex] be the length of the side of the square

Hence, The area of the square is given by

[tex]A = l^{2}[/tex]

Where [tex]A[/tex] is the area of the square

From the question, each side of a square is increasing at a rate of 5 cm/s, that is,

[tex]\frac{dl}{dt} = 5 cm/s[/tex]

Now, to determine the rate at which the area of the square is increasing, That is [tex]\frac{dA}{dt}[/tex]

To find [tex]\frac{dA}{dt}[/tex], differentiate [tex]A = l^{2}[/tex] with respect to [tex]t[/tex]

From, [tex]A = l^{2}[/tex]

[tex]\frac{dA}{dt} = \frac{d(l^{2}) }{dl}[/tex] ×[tex]\frac{dl}{dt}[/tex]

[tex]\frac{dA}{dt} = 2l[/tex] ×[tex]\frac{dl}{dt}[/tex]

Now, to determine the rate at which the area of the square is increasing when the area of the square is 36 cm²

First, we will determine the length at this instance,

From, [tex]A = l^{2}[/tex]

[tex]36 = l^{2}\\ \sqrt{36} = l\\6 = l\\l = 6cm[/tex]

The length at this instance is 6cm

To determine the rate at which the area of the square is increasing at this instance

[tex]l = 6cm\\[/tex]

From the question,  [tex]\frac{dl}{dt} = 5 cm/s[/tex]

Hence,

[tex]\frac{dA}{dt} = 2l[/tex] ×[tex]\frac{dl}{dt}[/tex]

[tex]\frac{dA}{dt} = 2(6)[/tex] × [tex]5[/tex]

[tex]\frac{dA}{dt} = 60 cm^{2}/s[/tex]

Hence. the area of the square is increasing at a rate of 60 cm²/s

Answer:

100 2/3

Step-by-step explanation:

50+50=100

1/3+1/3=2/3

100+2/3= 100 2/3

Answer:

Hey there! :)

Step-by-step explanation:

~Answer would be 100 2/3

(There is 3 steps for solving this question, the steps are provided below!)

Here is two ways you can solve this problem!:

Steps in order to solve this problem:

~ 1.Make both of the mixed number into a improper fraction.

151/3 + 151/3

~ 2.Now, when you add ‘151/3 + 151/3’ you will get 302/3.

~ 3.Finally you divide 302 and 3 which will give you 100 2/3

……………………………………………………………………………………………………

Another way to solve the question:

~1.Break up the mixed number:

50 1/3 = 50 + 1/3

50 1/3 = 50 + 1/3

~2.So this is the question you asked 50 1/3 + 50 1/3

Add 50+50 which gives you 100.

We solved for the whole number and now we have to solve for the fractions part.

1/3 + 1/3 = 2/3

~3.We got 100 as the whole and 2/3 as the fraction.

So now you just combine them both.

100 + 2/3 = 100 2/3

Therefore the answer is 100 2/3

Hope this helps!! I would be glad to help you with anything you don’t understand about this question! :D

Good luck!

Answer:

The answer is A) the speed at which the car has traveled

Step-by-step explanation: