Express as a trinomial.
(3x+5)(2x+9)

Answer:

First. 115°

Second. 65°

Third. 65°

Fourth. 7

Fifth. 425.25

First

angle DAB = angle ADC (since this is an isosceles trapezoid)

Second

In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)

180-115 is 65°

Third

(Same reason as second)

Fourth

The side 3x+4 is same as the opposite side

So 3x + 4 = 25

on solving you get x = 7 in

Fifth

[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]

area = 1/2 × 13.5 (20+43)

area = 1/2 × 13.5 × 63

Thus area is 425.25

Answer:

Step-by-step explanation:

1)As ABCD is isosceles trapezium,

∠ADC= ∠DAB

∠ADC = 115°

2) AD //BC

∠ADC + ∠DCB = 180°   {co interior angles}

115 + ∠DCB = 180

 ∠DCB = 180 - 115

 ∠DCB = 65°

3) As ABCD is isosceles trapezium,

∠CBA = ∠DCB

∠CBA = 65°

4) As ABCD is isosceles trapezium, non parallel sides are congruent.

AB = DC

3x + 4 = 25 in

3x = 25 - 4

3x = 21

x = 21/3

x = 7 in

5) height = 13.5 in

a= 43 in

b= 20 in

Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]

                   [tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]

Answer: x = 3

Step-by-step explanation:

Sqrt(x+7) - 1  = x

Sqrt(x+7) = x + 1

x+7 = x^2 + 1

x = x^2 - 6

x=3

Answer:

42 green marbles

Step-by-step explanation:

sum the parts of the ratio, 7 + 2 = 9 parts

Divide the number of marbles by 9 to find the value of one part of the ratio.

54 ÷ 9 = 6 ← value of 1 part of the ratio , then

7 parts = 7 × 6 = 42 ← number of green marbles

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5

Answer:

C

Step-by-step explanation:

As y is zero, y/x will be zero

Answer:

Infinite Amount of Solutions

Step-by-step explanation:

Since we have concurrent systems (same slope + same y-int), we know that the systems of equations would be the exact same line. If that is the case, the we would know that ANY value input would work. You could even test it mathematically, and it would give you infinite amount of solutions.

Answer: [tex]\large \boldsymbol {C) \ AB=\sqrt{41} }[/tex]

Step-by-step explanation:

Answer:

The correct option is;

C. -3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1

Please find attached the required function graph

Step-by-step explanation:

To solve the equation f(x) = 2·x⁴ + 12·x³ + 16·x² -12·x - 18, by graphing the function, we have;

x [tex]{}[/tex]       F(x)

-4[tex]{}[/tex]       30

-3[tex]{}[/tex]       0

-2[tex]{}[/tex]       6

-1[tex]{}[/tex]        0

0 [tex]{}[/tex]      -18

1[tex]{}[/tex]         0

2[tex]{}[/tex]       150

The shape of a graph with multiplicity of 2

Given that the graph bounces of the horizontal axis at the y-intercept at point x = -3, the factor (x - 3) must be a quadratic of the form (x - 3)², thereby having a multiplicity of 2 in the solution which are;

x = 1, -1, and, giving

(x - 1)·(x + 1)·(x - 3)² = 0

Therefore, the correct option is -3, multiplicity 2; -1, multiplicity 1; 1 multiplicity 1.

Answer:

C

Step-by-step explanation:

Answer:

C:-

[tex]\\ \sf\longmapsto c+115=180[/tex]

[tex]\\ \sf\longmapsto c=180-115[/tex]

[tex]\\ \sf\longmapsto c=65°[/tex]

D:-

[tex]\\ \sf\longmapsto d+70=180[/tex]

[tex]\\ \sf\longmapsto d=180-70[/tex]

[tex]\\ \sf\longmapsto d=110°[/tex]

a:-

f(x)=2x+3

[tex]\\ \rm\Rrightarrow f(1)=2(1)+3=2+3=5[/tex]

[tex]\\ \rm\Rrightarrow f(-5)=2(-5)+3=-10+3=-7[/tex]

[tex]\\ \rm\Rrightarrow f(a)=2a+3[/tex]

[tex]\\ \rm\Rrightarrow f(a+2)=2(a+2)+3=2a+4+3=2a+7[/tex]

[tex]\\ \rm\Rrightarrow f(b)=2b+3[/tex]

b:-

f(x)=x+4

[tex]\\ \rm\Rrightarrow f(-2)=(-2)+4=2[/tex]

[tex]\\ \rm\Rrightarrow f(3)=3+4=7[/tex]

[tex]\\ \rm\Rrightarrow f(7)=7+4=11[/tex]

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

C. $1,260

Step-by-step explanation:

80 × 14.5 = 1,160

2,500 × 0.04 = 100

Answer:

C. $1260

Step-by-step explanation:

Answer:

M<C = 20°

Step-by-step explanation:

Because they’re vertical angles, that means they’re equal to each other so:

m<C = m<D

x = -3x + 80

x + 3x = 80

4x = 80

x = 20

Since m<C equals x, that means m<C is 20°

A regular heptagon (7-sided figure) cannot be constructed with a compass and straightedge.

Answer:

C

Step-by-step explanation:

Its the only answer where the y intercept is 16.

We know its 16 because the line crosses the y axis at 16

Answer:

(i) a1/a2 =/ b1/b2

(ii) a1/a2=b1/b2 =/ c1/c2

(iii) a1/a2=b1/b2=c1/c2

Step-by-step explanation:

=/ means not equal to.

graphical repesentation of

1.intersecting lines

2.coincident lines

3.parallel lines

a1/a2 and next two slots is basically dividing the coefficents if each equation.

for eg. 1. a1/a2= 2/4=1/2 and so on.

parallel lines are inconsistent whereas intersecting and coincident lines are consistent.

Answer:

c. mean

Step-by-step explanation:

the data set that has less variation will have smaller distribution over a large area or variation measures.

Answer:

D. Interquile Range

Step-by-step explanation:

The datasets that have less variation are those that have smaller dispersion or variation measures.

Some of these measures of variance are variance, standard deviation, mean absolute deviation, range and interquartile range. Among the options shown, the only one that is used as a measure of variation is the interquartile range. The interquartile range is the difference between the third quartile and the first quartile of a data distribution. In other words, the interquartile range measures the range between the central 50% of the data.

For some reason, the scores your teacher gave you and the answer choices don't match up. I'm not sure why this is. Perhaps some kind of typo. Please double check and get back to me.

Answer:

x = 5

Step-by-step explanation:

x² - 5x = 0

(x² - 5x) /x = 0/x

x²/x - 5x/x = 0

x - 5 = 0

x = 5

Check:

x² - 5x = 0

5² - 5*5 = 0

25 - 25 = 0

The solution to the equation is:

x = 0 or x = 5

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

We have:

x²-5x = 0

We can solve the equation as follow:

x²-5x = 0

Factorize:

x(x - 5) = 0

x = 0 or (x -5) = 0

x = 0 or x = 5

Learn more about quadratic equation on:

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Answer & Step-by-step explanation:

Take the last  expression:

[tex](3*3)*(4*4)[/tex]

This can be simplified using exponents. [tex]x*x=x^2[/tex] :

[tex]3^2*4^2[/tex]

So, take the two numbers within the parentheses from the first expression and write separately, including the exponent with each. Do this with the next problem:

[tex](5*6)^3=5^3*6^3[/tex]

:Done

Answer:  Focus = (7.5, -3)

Step-by-step explanation:

The Vertex form of a horizontal parabola is: x = a(y - k)² + h   where

Rewrite the equation in Vertex form to identify a, h, & k:

2x = (y + 3)² + 14

[tex]x=\dfrac{(y+3)^2+14}{2}\\\\x=\dfrac{1}{2}(y+4)^2+7[/tex]

       Vertex: (h, k) = (7, -3)

         [tex]a=\dfrac{1}{2}[/tex]

Find p and then find the focus:  Focus = (h + p, k)

[tex]a=\dfrac{1}{4p}\quad \rightarrow \quad \dfrac{1}{2}=\dfrac{1}{4p}\quad \rightarrow \quad 4p=2\quad \rightarrow \quad p=\dfrac{2}{4}\quad \rightarrow p=\dfrac{1}{2}\\[/tex]

Focus: (7 + [tex]\frac{1}{2}[/tex] , -3) = (7.5, -3)

Answer:

The number to be added is 6.89

Step-by-step explanation:

Here, we want to know what number must be added to the expression to make it equal to zero.

Let the number be x

Thus;

-6.89 + 14.52 -14.52 + x = 0

-6.89 + x = 0

x = 6.89

Answer:

1. Data point A

4. Data point D

Step-by-step explanation:

In a scatter plot, the closer the clustered data points are close to the best line of fit, the greater the correlation that would exist between the two variables.

If we are to draw a best line of fit in the scatter plot that is shown above, the closest data points amongst data points A, B, C, D, and E, that would be close to the best line of fit are data points A and D.

Therefore, removing data point A and point D would cause the correlation to decrease the most.

Answer:

C. 178−−−√ m

Step-by-step explanation:

Given the following :

v = final velocity (in m/s)

u = initial velocity (in m/s)

a = acceleration (in m/s²)

s = distance (in meters).

Find v when u is 8 m/s, a is 3 m/s², and s is 19 meters

Using the 3rd equation of motion :

v^2 = u^2 + 2as

v^2 = 8^2 + 2(3)(19)

v^2 = 64 + 114

v^2 = 178

Take the square root of both sides :

√v^2 = √178

v = √178

Answer:

[tex]x + a = \frac{3}{4} \\ x = \frac{3}{4} - a[/tex]

for a:

[tex]a = \frac{3}{4} - x[/tex]

[tex]\\ \sf \longmapsto x+a=\dfrac{3}{4}[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{3}{4}-a[/tex]

[tex]\\ \sf \longmapsto x=\dfrac{3-4a}{4}[/tex]

And

[tex]\\ \sf \longmapsto a=\dfrac{3}{4}-x[/tex]

[tex]\\ \sf \longmapsto a=\dfrac{3-4x}{4}[/tex]

Answer:

0.34134

Step-by-step explanation:

in other to solve for this question we would be using the z score formula

z = (x - μ) / σ

x = raw score

μ = mean

σ = standard deviation

the question tells us to find the probability that a worker selected at random makes between $350 and $400

let x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50.

z1 = (x1 - μ) / σ = (350-400) / 50 = -1

z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0

from tables, P(z <= -1) = 0.15866

P(z <= 0) = 0.5

then the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 =

0.34134

that explains that the probability that a worker selected at random makes between $350 and $400 = 0.34134

The operating ratio of the local ice cream shop is 38 percent

The cost of goods sold is $2,500

The net sales is $18,200

The operating expenses is $4,350

The operating ratio can be calculated as follows

= cost of goods sold+ operating expenses/total revenue

= 2500+4,350/18,200

= 6,850/18,200

= 0.376×100

= 37.6

= 38%

Hence the operating ratio is 38%  

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{18 - 20}}\\\huge\boxed{=\mathsf{18 + (-20)}}\\\huge\boxed{\mathsf{= -2}}\\\huge\boxed{\textsf{Answer: 18 + (-20)}}\huge\checkmark\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

[tex]\\ \sf\longmapsto 7x-20=6x-1[/tex]

[tex]\\ \sf\longmapsto 7x-6x=-1+20[/tex]

[tex]\\ \sf\longmapsto x=-19[/tex]

Now

[tex]\\ \sf\longmapsto m<A=7x-20=7(-19)-20=133-20=113[/tex]

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

We can represent each ratio as a fraction, then use the cross products property to find the value of x.

[tex]\frac{3}{12} = \frac{x}{16} \\\\\\16\cdot3=48\\\\48\div12=4[/tex]

Hope this helped!