A triangle has a bottom left angle of (x + 15) degrees and a bottom right angle of (x degrees). 1 parallel and horizontal line sits at the top point of the triangle. Another parallel and horizontal line sits at the base of the triangle. The exterior angle to the bottom right angle of the triangle is (4 x minus 20) degrees.
What is the value of x?

Answer:

20

Step-by-step explanation:

Answer:

B) \(15\)

Step-by-step explanation:

\(f(x)=x^2-3x+5\)

\(f(-2)=(-2)^2-3(-2)+5\)

\(f(-2)=4-(-6)+5\)

\(f(-2)=4+6+5\)

\(f(-2)=10+5\)

\(f(-2)=15\)

Answer:

5%

Step-by-step explanation:

15/300 = 0.05

5%

The amount of ice cream consumed in the United State would be 5,650 millions of pounds in 2028.

Based on the information provided about the mount of ice cream consumed in the United State, a quadratic equation that models the amount of ice cream consumed, in millions of pounds, since 2010 is given by;

y = 12(x - 6)² + 3922

Where:

By substituting the value of y, the number of years can be calculated as follows;

5,650 = 12(x - 6)² + 3922

5,650 - 3922 = 12(x - 6)²

1728 = 12(x - 6)²

144 = (x - 6)²

12 = x - 6

x = 12 + 6

x = 18 years.

Since 2010; 2010 + 18 = 2028.

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Answer:

3.9

Step-by-step explanation:

a^2+b^2=c^2

a^2+7^2=10^2

a^2+49=100

100-49=a^2

\(\sqrt{51}\)=a

x^2+6^2=a^2

x^2+36=\(\sqrt{51}\)^2

x^2+36=51

51-36=x^2

15=x^2

\(\sqrt{15}\)=x

x=3.9

Answer:

23+19+27+x = 96

x > 27

not sure if the answer can be left that way or do you assume that test results are whole numbers, if so then the answer  would b=have to be 28.. but I think that >27 is the answer expected

Step-by-step explanation:

A perfect square means that the given value is the result of the multiplication of an integer with itself, for example 2*2=4 →√

Answer:

Rotation 90 degrees counter clockwise, dilation of 6, translation down

Step-by-step explanation:

There are 120 boats in the marina using algebraic equation.

We shall represent the number of boats in the marina with the letter x so that we derive an algebraic equation to solve for x as follows:

number of white boats = 5x/6

number of blue boats = 2/5 of (x - 5x/6)

number of blue boats = 2/5 × x/6

number of blue boats = x/15

number of red boats = 12

so that;

5x/6 + x/15 + 12 = x

LCM of the denominators is 30

(25x + 2x + 360)/30 = x

27x + 360 = 30x {cross multiplication}

30x - 27x = 360 {collect like terms}

3x = 360

x = 360/3 {divide through by 3}

x = 120

Therefore, there are 120 boats in the marina using algebraic equation.

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Answer:

Since we know that,

cos2x= cos²x-sin²x=(cosx-sinx)(cosx+sinx)

And, sin2x=2sinx.cosx

Therefore,

1-sin2x= cos²x+sin²x-2sinx.cosx

1-sin2x= (cosx-sinx)²

Then let

y=cos2x/(1-sin2x)

Answer:

y=1/5x-7

Step-by-step explanation:

Answer:22:2x10x10x10x10x10x10x10x10x10x10... 23:3.4x10 divided by 2.... 24:1.5x10 divided by 9...... 25:5.9x10x10x10x10x10x10x10x10x10x10.... 26: 4.8 x 10 divided by 3..... 27: 6.25x10x10x10x10x10.

Step-by-step explanation:I divide because on some of them it's a negative power so instead of multiplying I'll divide. Hope this helps

Answer:

5 13/8 or 6 5/8

Step-by-step explanation:

2 3/4 + 3 7/8

since we are add we need to get a common denominator(bottom number)

I know that 2 × 4 = 8

3/4 × 2 = 6/8

new problem is

2 6/8 + 3 7/8

2+3=5

6/8 + 7/8 = 13/8

5 13/8

you may need to simplify you answer

13 - 8 = 5

6 5/8

Answer:

Step-by-step explanation:

*if this is wrong its because they didnt line the square up properly*

But the answer os 28 because, what you will need to do is multiply side and top

The side has 4 squares in the box

and the top has 7

so multipy 7 x 4 or 4 x 7

7 x 4 = 28

The figure with the vertices G(-4,1), H(4,1) and I(0,-2) is an isosceles triangle , the perimeter is 18 cm and the area is 12cm² .

In the question ,

it is given that

On plotting the vertices , we can see that the vertices form a triangle .

the graph is shown below.

to find the the Perimeter and Area we need length of triangle ,

given vertices G(-4, 1), H(4, 1), I(0, -2)

So ,

length of GH=√(4-(-4))²+(1-1)² = √8² = 8

length of HI = √(0-4)²+(-2-1)² = √16+9 = √25 = 5

length of GI = √(0-(-4))²+(-2-1)² = √16+9 = √25 = 5

As we can see that two sides of the triangle are equal , hence the figure is an isosceles triangle .

The Perimeter of the triangle GHI = GH+HI+GI

                                                        = 8+5+5

                                                         = 18 cm

For Area we need the height of the triangle

A is the mid point of GH so , GA = AH = 4

We calculate height(IA)=h using the Pythagoras Theorem in ΔHAI

IH²=IA²+AH²

substituting the values , we get

5²=h²+4²

25 = h² + 16

h² = 25-16

h² = 9

h = 3

hence the height of the triangle is 3 cm

Area of triangle GHI = (1/2)×Base×Height

= (1/2)×8×3

= 12

hence the area is 12 cm².

The figure with the vertices G(-4,1), H(4,1) and I(0,-2) is an isosceles triangle , the perimeter is 18 cm and the area is 12cm² .

The given question is incomplete , the complete question is

Identify the figure with the given vertices. Find the perimeter and area of the figure.

G(-4, 1), H(4, 1), I(0, -2).

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The ratio of the two point is the coordinate at the plane where the two point are divided at the fixed amount of length. The y value of the point that is 3/4 distance from point E to point F is -1.5. thus the option 4 is the correct option.

Given information-

The coordinates of the point E is (2,-3).

the coordinates of the point F is (-2,-1).

As the 3/4 the distance from the point E is the point F is means the points which divides the line EF in the ratio of 3/1.

The ratio of the two point is the coordinate at the plane where the two point are divided at the fixed amount of length.

Suppose the ratio \(m:l \) are the ratio of the two points \((x_1,y_1)\) and \((x_2,y_2)\). Then the coordinate of the point which divide the line at this ratio can be given as,

\((x,y)=\left ( \dfrac{mx_2+lx_1\tiems}{m+l} ,\dfrac{my_2+ly_1}{m+l} \right )\)

Put the values,

\((x,y)=\left ( \dfrac{3\times (-2)+1\times(2)}{3+1} ,\dfrac{3\times (-1)+1\times(-3)}{3+1} \right )\)

\((x,y)=(-1,-1.5)\)

Thus the y value of the point that is 3/4 distance from point E to point F is -1.5. thus the option 4 is the correct option.

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Answer:

the two opposite angles equal 45 and the other two who are twice the amount is 90

Step-by-step explanation:

sum of angles in a quadrilateral is 360. Lets name the two equal diagonal angles x that means the equation wil be

x+x+2x+2x=360

8x=360

x=45

so the equal diagonal ones will be 45 and the other two angles will be twice as much so 45x2=90

Answer:

a. y = 3 × (x + 2)(x - 8)

b.  y = 3·(x - 3)² - 75

c) y =  3·x² - 18·x - 48

Step-by-step explanation:

The x-intercept of the quadratic equation are (-2, 0), (8, 0)

The stretch of the quadratic equation = 3

We have;

a. The factored form y = 3 × (x + 2)(x - 8)

b. From the vertex form, we have;

y = 3 × (x + 2)(x - 8) = 3·x² - 18·x - 48

y = 3·x² - 18·x - 48

The vertex form a(x - h)² + k

Where;

h = -b/(2·a) = 18/6 = 3

h = 3

k = c - b²/(4·a) = -48 - (18²)/12 = -75

The vertex form 3·(x - 3)² - 75

c) The standard form of the quadratic equation, y = a·x² + b·x + c

The standard form of the quadratic equation is y =  3·x² - 18·x - 48.

Answer:

Step-by-step explanation:

The line perpendicual to a reference line will have a slope that is the negative inverse of the reference line.  In this case, the reference line is y= -(1/3)X+8, with a slope of -(1/3).  The negative inverse would be 3.  So the new line would have the form:

y = 3x + b

To find b, the y-intercept, use the given point and solve for b:

y = 3x + b

or 8 = 3*3 + b for the point (3,8)

8=9+b

b= -1

Thje equation of the line perpendicualr to the reference line and going through point (3,8) is:

y = 3x - 1

See attached graph.

Answer:

The second choice is correct

Step-by-step explanation:

Here, we want to get the correct statement

As can be seen, while 2 is the angle at the circumference, 1 is the angle at the center

Mathematically, we know that angle at the center is two times the angle at the circumference

Thus,

m1 = 1/2 (m2)

or m2 = 2 * m1

Answer:

15 feet

Step-by-step explanation:

-1.5 × 10 = -15

so -15 = 15 feet deep.

have a nice day!

The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

Answer:

b=37

Step-by-step explanation:

if the angles are supplementary then they will add up to equal 180.

to find b you just subtract 143 from 180 to get 37

Answer:

4(x + 3)

Step-by-step explanation:

So, to solve these questions is pretty simple.

4 times what equals 4x, and 4 times what equals 12?

Well,

4 times x  = 4x, and 4 times 3 = 12.

soo.

4(x + 3)

Answer:

4x+12  factor 4 out of the equation

19) : -7x=5.6⇒ x=-5.6/-7

x/8- 5/2=5/2 common factor

(x-20)/8 =5/2

2(x-20)=40

2x-40=40

2x=80

Answer: 9

Step-by-step explanation:

Formula : Mean = \(\dfrac{\text{Sum of observations}}{\text{Number of observaions}}\)

Given: 5 students participated in a push-up competition.

The amount of push-ups each student completed is listed: 12, 7, 10, 11,5.

Mean = \(\dfrac{12+7+10+77+5}{5}\)

\(=\dfrac{45}{5}=9\)

Hence, the mean number of push-ups = 9

Answer:

The cost of 4 dozen eggs is 4 * $1.25 = $5.

The cost of half a gallon of milk is $2.97.

The total cost of the eggs and milk is $5 + $2.97 = $7.97.

Since Chase has only $10, the minimum price for a dozen eggs is $10 - $7.97 = $2.03.

So the answer is 2.03

Step-by-step explanation:

A. statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

B. the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

C. Both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

(a) To test the hypothesis that there is a difference in the population means between breast-fed infants and formula-fed infants, we can use a two-sample t-test with equal variances. The null hypothesis is that the population means are equal, and the alternative hypothesis is that they are not equal. Using α = 0.05 as the significance level, the critical value for a two-tailed test with 40 degrees of freedom is ±2.021.

The test statistic can be calculated as:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))

where x1 and x2 are the sample means, Sp is the pooled standard deviation, and n1 and n2 are the sample sizes. The pooled standard deviation can be calculated as:

Sp = √(((n1 - 1) * s1² + (n2 - 1) * s2²) / (n1 + n2 - 2))

where s1 and s2 are the sample standard deviations.

Plugging in the values from the table, we get:

t = (13.3 - 12.4) / (1.776 * √(1/23 + 1/19)) = 2.21

Since the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference in the mean blood hemoglobin levels between breastfed infants and formula-fed infants at α = 0.05.

(b) To construct a 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants, we can use the formula:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

where tα/2,Sp is the critical value of the t-distribution with (n1 + n2 - 2) degrees of freedom and α/2 as the significance level.

Plugging in the values from the table, we get:

(x1 - x2) ± tα/2,Sp * √(1/n1 + 1/n2)

= (13.3 - 12.4) ± 2.021 * 1.776 * √(1/23 + 1/19)

= 0.56 ± 0.62

Therefore, the 95% confidence interval for the difference in population means between breast-fed infants and formula-fed infants is (−0.06, 1.18).

(c) The hypothesis test and the confidence interval both lead to the conclusion that there is a difference in the mean blood hemoglobin levels between breast-fed infants and formula-fed infants. In part (a), we rejected the null hypothesis that the population means are equal, which means we concluded that there is a difference. In part (b), the confidence interval does not contain 0, which means we can reject the null hypothesis that the difference in means is 0 at the 95% confidence level.

Therefore, both the hypothesis test and the confidence interval lead to the same conclusion that there is a difference in the mean blood hemoglobin levels between the two feeding regimens.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here is real answer :>