Write an algebraic equation to match each graph. (These graphs are not drawn to scale!)

Answer:

[tex]\frac{35(1 + 35)}{2}[/tex]

Step-by-step explanation:

Given:

The attached

Required

Find the equivalent expression

The interpretation of is to add the sequence:

n = 1,2,3,......35

This can be done using the following formula (Sum of n terms of an AP)

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where n is the number of terms from 1 to 35; [tex]n = 35[/tex]

T1 is the first term; [tex]T_1 = 1[/tex]

Tn is the last term; [tex]T_n = 35[/tex]

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex] becomes

[tex]S_n = \frac{35}{2}(1 + 35)[/tex]

[tex]S_n = \frac{35(1 + 35)}{2}[/tex]

From the list of given options;

Option A is correct

[tex]\frac{35(1 + 35)}{2}[/tex]

Answer:

x=25°

Step-by-step explanation:

sin (x+22)=cos(2x-7)=sin (90-(2x-7))

x+22=90-(2x-7)

x+22=90-2x+7

x+2x=97-22

3x=75

x=75/3=25°

Answer:

x = 25

Step-by-step explanation:

Recall the trig identity sin(x) = cos(90 - x)

In other words, sin(x + 22) = cos(90 -(x+22)) = cos(68 - x)

Now, set them equal to each other:

cos(68 - x) = cos(2x - 7)

We can ignore the cosine:

68 - x = 2x - 7

3x = 75

x = 25

Answer:

Wet Suit Willy found the most treasures per dive.

Step-by-step explanation:

Given:

Diver name         Number of dive    Number of boxes

Sam                                  11                        33

Wet Suit Willy                  18                        81

Deep Diving Dan            26                       104

Find:

Who found the most treasures per dive

Computation:

Sam's per dive collection = 33 / 11 = 3 boxes

Wet Suit Willy's per dive collection = 81 / 18 = 4.5 boxes

Deep Diving Dan's per dive collection = 104 / 26 = 4 boxes

Wet Suit Willy found the most treasures per dive.

Answer: 197

Step-by-step explanation: square 28 + square 195 = x squared so then find the sqrt of that

Answer:

80 lamps

Step-by-step explanation:

number of lamp bases*no. of lampshades*no. of lightbulbs= total number of lamp choices

5*(3*3)*2

=5*9*2

=40*2

=80

hope it helps :)

Answer:

7.5 feet

Step-by-step explanation:

If we look at the yellow line, it is 6 cm.

To find how many times 2cm goes into 6cm, we divide.

[tex]6\div2=3[/tex]

So, if we reproduce the shape for every 2 cm, we have to multiply the value by 3.

Since every 2 cm will be equal to 2.5 feet, we can multiply the values.

[tex]2.5\cdot3=7.5[/tex]

So Jackie should make the yellow line 7.5 feet long.

Hope this helped!

Answer:

The answer is 7.5 feet

Step-by-step explanation:

Kakadk.

Answer for problem 1: slope = 2, y intercept = 3

Answer for problem 2: slope = 3/4, y intercept = -2

Explanation:

Both equations are in the form y = mx+b. This is known as slope intercept form. This is because we can read off the values of the slope and y intercept very quickly. We have y = 2x+3 match up with y = mx+b. The m is the slope and b is the y intercept. So m = 2 and b = 3 for this equation. A similar situation happens with the other equation as well. It might help to rewrite the second equation into y = (3/4)x + (-2).

Answer:

slope: 1.) 2 ,,, 2.) 3/4

y-int: 1.) (0,3) ,,, 2.) (0,-2)

graph: attached in pictures/ blue line represents y=2x+3 ,,, red line represents y=3/4-2

Step-by-step explanation:

Answer:

5x+2y=48 or 5x-12y=-8

The value of x is 5 and y is 4.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

The Equations are:

5x - 12y= -8...................(1)

and, 5 x + 2 y = 48 ..................(2)

Solving the Equation (1) and (2) we get

-12y -2y = -8 - 48

-14y = -56

y= -56 /(-14)

y = 4

and, 5x +2y= 48

5x + 8 = 48

5x= 40

x= 5

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Answer:

45

Step-by-step explanation:

20 boys= 5 times the ratio

So, 5x5=25

25 girls and 20 boys= 45 students

Answer:

45 students

Step-by-step explanation:

to make sure there are 20 boys you need to multiply 4 by 5

so multiply the 5 by 5 as well

then add what you get!!

Answer: she needs to work 8 hours

Step-by-step explanation:

Answer:

When x = 7, y = 4

Step-by-step explanation:

We are simply looking for the y-value for when the graph input x equals 7. When we look at the graph when x = 7, we see that our y-value y equals 4.

Answer:

x=7 y=4

Step-by-step explanation:

Answer:

y=x+-2

Step-by-step explanation:

Slope intercept form is y=mx+b

I plugged in the slope for m and y-intercept for b

sorry i did this real fast because it sounded urgent :)

Answer:

2

Step-by-step explanation:

The constant of variation is 2 because the variable is x, and its coefficient, 2, is the constant of variation.

Answer:

35 red marbles

Step-by-step explanation:

So we can put the different color marbles in a ratio. So 7:2:11. If we add all of those up we get 20. We do 100/20 to get 5. Each number in the ratio is equivalent to 5 marbles. Then we do 7*5 to get 35. We can check our work by doing, (7*5) + (2*5) + (11*5) = 100. And it does equal 100 so the answer is correct.

Answer:

35 red marbles

Step-by-step explanation:

The total number of marbles the student recorded is 20

Now we have to make a ratio of red to the total number of marbles

That would be 7 : 20

After this, there will be a new ratio which is x : 100

Lastly we will solve for x making the equation 20x = 700, x = 35

Answer:

2 and -2

Step-by-step explanation:

● 7q^2 -28 = 0

Add 28 to both sides

● 7q^2-28+28 = 28

● 7q^2 = 28

Divide both sides by 7

●7q^2/7 = 28/7

● q^2 = 4

You can write directly q= 2 or q= -2

To understand it use the absolute value.

● |q| = 2

● q = 2 or q = -2

The solutions are {2, -2}

Answer:

20

Step-by-step explanation:

Answer:

B. 1 must be a root of the polynomial 3x^2+x-4

Step-by-step explanation:

Given polynomial

3x^2+x-4

Divided by factor x-1

Gives a remainder of 0

Remainder 0 represents that divisor (x-1) is a factor polynomial 3x^2+x-4

If x-1 is a factor of the polynomial, we can equate x-1 to 0

x-1=0

Solve for x to get one of the roots

x-1=0

Add 1 to both sides

x-1+1=0+1

x=1

B. 1 must be a root of the polynomial 3x^2+x-4

Answer:

[tex]2h^{2} + 7hk - 15k^{2}[/tex]

Step-by-step explanation:

Distribute (2h − 3k)(h + 5k).

2h^2 + 10hk - 3hk - 15k^2

2h^2 + 7hk 15k^2

Answer:

B 2/5

Step-by-step explanation:

Used a calculator.

Answer:

10+6=16

16*25=400

400+4=404

Step-by-step explanation:

EZ...

Answer:

I Think it is the 3rd equation

Step-by-step explanation:

When you have two congruent figures, the vertices are listed in the same order. This means that

Side LM ≅ Side QR, Side MN ≅ Side RS, etc. The same applies for the angles.

Therefore, Side LM ≅ Side QR and Angle MNO ≅ Angle RST.

The complete statements are Side LM is congruent to the side QR and angle ∠MNO is congruent to angle ∠RST.

The two quadrilaterals whose angles and sides of one quadrilateral are the same as the corresponding angles and sides of another quadrilateral then two quadrilaterals are congruent to each other.

The order of the lettering for congruent parts should place the lettering for corresponding parts in the same order.

Given in the question that the quadrilateral LMNO and QRST are congruent.

LMNO ≅ QRST

As we know Congruent Parts of the congruent Figures are also congruent, we have;

side LM is congruent to side QR.

side MN is congruent to side RS.

side NO is congruent to side ST.

side OL is congruent to side TQ.

Similarly, for the corresponding angles of the quadrilaterals, we have;

angle ∠MNO is congruent to angle ∠RST.

angle ∠NOL is congruent to angle ∠STQ.

angle ∠OLM is congruent to angle ∠TQR.

angle ∠LMN is congruent to angle ∠QRS.

Therefore, Side LM is congruent to the side QR and angle ∠MNO is congruent to angle ∠RST.

Learn  more about Congruent quadrilateral

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Answer:

12 cm

Step-by-step explanation:

You would only have to focus on the green line and then you just have to divide it by 12 and you get 4 and than you multiply 3 cm by 4 and the answer for the actual length of the green line will be 12 cm.

Answer:

12 cm

Step-by-step explanation:

The ratio of feet to cm is 12:3. Set up a ratio to find the length of the green line in cm.

12 feet ÷ 3 cm = 48  ft ÷ x

Cross multiply and divide.

3 x 48 = 12 × x

144 = 12x

x = 12

The actual length of the green line is 12 cm.

Hope that helps.

Answer:

The linear factors are:

[tex]x - 2[/tex]

[tex]x + 3[/tex]

[tex]x + 1[/tex]

Step-by-step explanation:

Given

[tex]x^3 + 2x^2 - 5x - 6[/tex]

Required

Select all linear factors of the polynomial

Solving for x - 2;

Equate x - 2 to 0 and solve for x

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

[tex]x = 2[/tex]

Substitute 2 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]

[tex]2^3 + 2(2^2) - 5(2) - 6[/tex]

[tex]= 8 + 8 - 10 - 6[/tex]

[tex]= 0[/tex]

Because, we arrived at 0, then x - 2 is a factor

Solving for x + 3;

Equate x + 3 to 0 and solve for x

[tex]x + 3 = 0[/tex]

[tex]x = -3[/tex]

Substitute -3 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]

[tex](-3)^3 + 2(-3^2) - 5(-3) - 6[/tex]

[tex]= -27 + 2(9) + 15 - 6[/tex]

[tex]= -27 + 18 + 15 - 6[/tex]

[tex]= 0[/tex]

Because, we arrived at 0, then x + 3 is a factor

Solving for x - 1;

Equate x - 1 to 0 and solve for x

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

[tex]x = 1[/tex]

Substitute 1 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]

[tex](1)^3 + 2(1^2) - 5(1) - 6[/tex]

[tex]= 1 + 2(1) - 5 - 6[/tex]

[tex]= 1 + 2 - 5 - 6[/tex]

[tex]= -8[/tex]

Because, we did not arrived at 0, then x - 1 is not a factor

Solving for x + 1;

Equate x + 1 to 0 and solve for x

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

[tex]x = -1[/tex]

Substitute -1 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]

[tex](-1)^3 + 2(-1^2) - 5(-1) - 6[/tex]

[tex]= -1 + 2(1) + 5 - 6[/tex]

[tex]= -1 + 2 + 5 - 6[/tex]

[tex]= 0[/tex]

Because, we arrived at 0, then x + 1 is a factor

Answer:

Hello There. ☆~\《`°---_●£●__---`°》\~☆

An exponential growth function is represented by

f(x)=a(b)^{x},a>0,b>1.

The given functions can be written as,

A)f(x)=.001(1.77)^x,0.001>0,1.77>1

B)f(x)=2(1.5)^{x/2}=2(\sqrt{1.5} )^x,2>0,\sqrt{1.5} >1

C)f(x)=5(0.5)^{-x}=5(2)^x,5>0,2>1

D) f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e.

So the function f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e violates the conditions for an exponential growth function. It is an exponential decay function.

The correct choices are (A), (B), (C).

Hope It Helps!~ ♡

ItsNobody~ ☆

The functions that represent exponential growth are choices (A), (B), and (C). The correct option is A, B, and C.

Exponential growth is the process of gradual increase of quantity over time.

An exponential growth function is represented by

[tex]\rm f(x)=a(b)^{x}[/tex],  a>0,b>1

The given functions can be written as,

A)[tex]f(x) = .001(1.77)^x[/tex], 0.001>0,1.77>1

B) [tex]f(x) = 2(1.5)^{x/2} = 2(\sqrt{1.5} )^x,[/tex]   2>0,  [tex]\sqrt{1.5}[/tex] >1

C)[tex]f(x) = 5(0.5)^{-x}=5(2)^x[/tex],    5>0, 2>1

D) [tex]f(t) = 5e^{-t}=5(\frac{1}{e} )^x[/tex],        5>0,  1/e.

So, the function [tex]f(t)=5e^{-t}=5(\frac{1}{e} )^x,5 > 0,1/e[/tex] violates the conditions for an exponential growth function. It is an exponential decay function.

The correct choices are (A), (B), and (C).

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Answer: y = -1/2x -1

Step-by-step explanation: since the new line is parallel to the given line the slope of both the lines world be same. Therefore putting the new values in the equation

y-y1=m(x-x1)

y-1=-1/2(x+4)

y-1=-1/2x -2

y=-1/2x-1

Answer: A. 9

Step-by-step explanation:

In the given tree diagram , there are 3 branches , to each branch there are 3 leaf nodes.

By using Fundamental counting principal ,

Number of possible outcomes for the tree diagram = (Number of branches) x (Number of leaf nodes)

[tex]=3 \times 3\\\\=9[/tex]

Hence, the number of possible outcomes for the tree diagram = 9

So, the correct option is A. 9.

Answer:

[tex]\boxed{70\°}[/tex]

Step-by-step explanation:

Angle ABP and angle MAB are corresponding angles.

Corresponding angles are equal.

Angle ABP = 50 degrees

Angle CBP and angle BCQ are corresponding angles.

Corresponding angles are equal.

Angle CBP = 20 degrees

Angle ABC is the sum of angles CBP and ABP.

[tex]50+20=70[/tex]

Answer:

[tex]\large \boxed{\sf \ \ A=5, \ \ B=-13 \ \ }[/tex]

Step-by-step explanation:

Hello,

What you did is correct...

[tex](Ax-3)(x-2)=5x^2+Bx+6\\\\\text{*** we develop the left side ***}\\\\Ax^2+(-2A-3)x+6=5x^2+Bx+6[/tex]

... and you found A by identifying the term in [tex]x^2[/tex] to get A = 5, right?

What about the other terms?

We can then identify the like terms:

>>> term in [tex]x^2\\[/tex]

   A = 5

>>> term in x

   -2A+3=B

>>> constant term

   6 = 6

As we know that A=5 it means that B = -2*5-3=-13

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

B = -13

Step-by-step explanation:

Nothing is wrong you just have to complete it..

soo continuing from where you stopped.

Ax² - 2Ax - 3x + 6 = 5x² + Bx + 6

(its supposed to be the equivalence sign [with three dashes] but I am restricted by my keypad, so I made use of the equal to sign [two dashes])

comparing both sides, we can therefore say:

Ax² = 5x²..............i

- 2Ax - 3x = Bx......ii

+6 = +6..............iii

sub the value of A = 5 into ......ii

-2Ax - 3x = Bx

-2(5)x - 3x = Bx

-10x - 3x = Bx

-13x = Bx

B = - 13